LOBACHEVSKY, b5'bh-ehg'ske, NIKOLAI TVANOVITCII (1793-1S56). A Russian mathema tieian, born at Nijni-Novg.orod. the son of a peas ant. He studied at Kazan, where he became adjunct professor of mathematics in 1314 and professor in 1:316. He held this position for forty years, and for nineteen years lie was rector of the university. In 1829-30 lie published the first geometry which was not based upon the Euclidean postulate of parallel lines I see the article GEOMETRY) , ;Bid dills became the foun her of the Non-Euclidean geometry. see also DoL YA1.) His works are as follows: Pr:a, Eph s of Geometry (original in Russian. ; maginary Geometry (original in Russian. Is35) Principles of GI with Theory of Parallels (original in Rus,ian, 38) ; Geometrisehe Untersuch nay( n t-ur The uric der Parallellinien (original in German. 1340; new German ed. 1887, English trans. 13911: Pnngr'ometrie ou preccis fond(' .stir tine tluuric gCnerale et riyoureuse des parallelc• (original in French, 1S551. His complete work: were
edited by Janisehevsky (1370:, and have been translated by Boiiel. Battaglini, and Halsted. A collection of his geometrical writings appeared in Kazan. The first volume of this collection, published in 1883, contains Lobachersky's Rus sian articles only and bears a Russian title; the second and last volume, published in 1886, con tain, his French and German articles. and, be sides the Russian title, hears al,o the following title in French: rielleet ion complete des rp'omitriques do N. I. Lobatehe ff sky. Consult: Holid, in the hull, tin des s (1S79 ; Vassilieff, Eloye historique de Nicolas Lobatellersk y (English trans. Austin. Tex.. 1394 . For his geometry, consult New Principles of Geometry, with Complete Theorfi of Parallels. translated from the Russian by Halsted (Austin, Tex., 1897).