Nicolai Ivanovich Lobachevskii, the other discoverer of non-Euclidean geometry, lived and worked in Kasan in Russia, and when circumstances permitted started by 1830 to publish accounts of his new geometry. This early essay is looked at briefly: it derives the crucial trigonometric formulae from a consideration of the intrinsic differential geometry of the new geometry. This work is seldom described in recent histories of mathematics. Lobachevskii’s later, and better known, work in his Geometrische Untersuchungen (1840) is compared with the treatment given by János Bolyai.
Extract: a lengthy extract from the conclusion to Lobachevskii’s Geometrische Untersuchungen.
KeywordsEuclidean Geometry Good Mathematician Trigonometric Formula Congruent Sphere Stellar Parallax
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