This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.

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H.S.M. Coxeter (1907-2003) was Professor of Mathematics at the University of Toronto.

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