Translation of Lobachevsky’s papers on non-Euclidean geometry

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Nikolai I. Lobachevsky, The Foundations of Geometry: Works on Non-Euclidean Geometry (Minkowski Institute Press, Montreal 2019), 210 pages


Neither general relativity (which revealed that gravity is merely manifestation of the non-Euclidean geometry of spacetime) nor modern cosmology would have been possible without the almost simultaneous and independent discovery of non-Euclidean geometry in the 19th century by three great mathematicians – Nikolai Ivanovich Lobachevsky, Janos Bolyai and Carl Friedrich Gauss (whose ideas were later further developed by Georg Friedrich Bernhard Riemann).

This volume contains three works by Lobachevsky on the foundations of geometry and non-Euclidean geometry: “Geometry”, “Geometrical investigations on the theory of parallel lines” and “Pangeometry”. It will be of interest not only to experts and students in mathematics, physics, history and philosophy of science, but also to anyone who is not intimidated by the magnitude of one of the greatest discoveries of our civilization and would attempt to follow (and learn from) Lobachevsky’s line of thought, helpfully illustrated by over 130 figures, that led him to the discovery.