The first authors of non-Euclidean geometries were the Hungarian mathematician János Bolyai and the Russian mathematician Nikolai Ivanovich Lobachevsky, who separately published treatises on hyperbolic geometry around 1830. As well Eugenio Beltrami published book on non-Eucludean geometry in 1868. Others, such as Carl Friedrich Gauss, had earlier ideas, but did not publish their ideas at the time.= = = Miranda de Ebro = = =
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