Worlds out of Nothing: A Course on the History of Geometry in the 19th Century.
Springer Undergraduate Mathematics Series.
A history of synthetic and algebraic projective geometry, non-Euclidean geometry, and axiomatic geometry 1789—1914. Mathematicians whose work is discussed included Poncelet, Chasles, Gauss, Bolyai, Lobachevskii, Plücker, Hesse, Riemann, Beltrami, Klein, Poincaré, Pasch and Hilbert. There is a discussion of several philosophies of geometry, and the relation of geometry to physics in the early work of Einstein. The book is written as a lecture course, with extensive advice on how to write essays in the subject.
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