Non-euclidean geometry — A re-interpretation

SummariesThe researches into non-Euclidean geometry from Saccheri 1733 to Riemann 1854 and Beltrami 1868 can best be understood not merely as foundational enquiries, but also as a progressive elaboration of the methods of analysis and later of differential geometry. The hyperbolic trigonometry of Lobachevskii and J. Bolyai was not generally taken as a conclusive demonstration of the existence of non-Euclidean geometry until it was given a foundation in the study of intrinsic Riemannian geometry