(1) Born at Nijni-Novgorod, November 2 (October 22, o.s.), 1793; died at Kazan, February 24(February 12), 1856. The name is transliterated from the Russian in various ways, such as Lobatschevskij, Lobatschewsky, and Lobatcheffsky.

(2) Ueber die Principien der Geometrie Kazan, 1829-1830; Geometrische Untersuchungen zur Theorie der Parallellinien, Berlin, 1840; Fench translation by Houel, 1866; English by Halste, 1891; Pangeometrie ou Precis de geometrie fondee sur une theorie generale et rigoureuse des paralleles, Kazan, 1855. He also published carious memoirs on other subjects. Vassilief's eulogy on Lobachevsky has been translated into French (1896) and English (1894).

(3) On Bolyai's appreciation of Lobachevsky's work, see Stackel, loc. cit., I, 140.