Non-Euclidean geometries: Gauss, Lobachevskiĭ and Bolyai. (Spanish:Las Geometrías no euclídeas: Gauss, Lobatchewsky y Bolyai)

Abstract

The author presents the origin of non-Euclidean geometry in the works of J. Bolyai, C. F. Gauss and N. I. Lobachevskiĭ. The main ideas from the Appendix by Bolyai (1831) and from Pangeometria by Lobachevskiĭ (posthumous, 1855) and the reaction of Gauss to the publications of Lobachevskiĭ and Bolyai are presented. The paper contains many excerpts from the works of Lobachevskiĭ and Bolyai and from the letters of Gauss and Bolyai. The exposition is illustrated with many figures. Brief biographies of Bolyai and Lobachevskiĭ are also included.