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LOBACHEVSKII, Nicolai Ivanovitch (1793-1856). "O nachalakh geometrii" [in Russian], in:

5 parts bound in one volume, 8o (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).

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

"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 Lobachevskian geometry at a slightly later date than Lobachevsky; he explained his discovery in an appendix to his father's work that was published in 1832 [see lot 942]. (Since Gauss did not publish his work on the subject, and since Bolyai published only at a later date, Lobachevsky clearly holds priority.)" (DSB).

The unique applicability of Euclidean geometry to the real world was refuted by Lobachevskii's system. His contribution, along with Gauss, Bolyai, and Riemann, shook the foundations of geometry as accepted since Greek times and led the way to the Einsteinian concept of variably curved space--"the most consequential and revolutionary step in mathematics since Greek times" (Kline, p. 879). "The geometry of the real world is that of variable curvature, which is on the average much closer to Lobachevsky's than to Euclid's" (DSB).

Grolier/Horblit 69a; Kline, pp. 873-81; PMM 293a; Norman 1379.

*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

*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 Lobachevskian geometry at a slightly later date than Lobachevsky; he explained his discovery in an appendix to his father's work that was published in 1832 [see lot 942]. (Since Gauss did not publish his work on the subject, and since Bolyai published only at a later date, Lobachevsky clearly holds priority.)" (DSB).

The unique applicability of Euclidean geometry to the real world was refuted by Lobachevskii's system. His contribution, along with Gauss, Bolyai, and Riemann, shook the foundations of geometry as accepted since Greek times and led the way to the Einsteinian concept of variably curved space--"the most consequential and revolutionary step in mathematics since Greek times" (Kline, p. 879). "The geometry of the real world is that of variable curvature, which is on the average much closer to Lobachevsky's than to Euclid's" (DSB).

*Kazanskii vestnik*apparently had a small circulation even within Russia, which undoubtedly contributed to the initial lack of attention to Lobachevskii's writings commanded from the scientific community, and accounts for the paucity of copies known to exist either in public or private libraries. For the 1958 Grolier Club's exhibition "One Hundred Books Famous in Science," it was necessary to borrow a set of the journal issues from a Soviet library (either the A.M. Gorki Library of Science or the Moscow University Library), and the organizers of the "Printing and the Mind of Man" exhibition (1963) found the original edition "unprocurable" and displayed only the 1887 German translation. The Norman copy is the only known copy in North America (and presumably the Western Hemisphere). There is no known copy of it in Europe, and it is unclear how many complete copies exist in Russia. OF THE GREATEST POSSIBLE RARITY.

Grolier/Horblit 69a; Kline, pp. 873-81; PMM 293a; Norman 1379.