Wolfe H.E. Introduction to Non-Euclidean Geometry

New York, USA: The Dryden Press, 1945 (Reprint 2012). — 274 p. — ISBN: 0486498506.One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.
Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistency of the non-Euclidean geometries. Extensive appendixes offer background information on the foundation of Euclidean geometry, circular and hyperbolic functions, the theory of orthogonal circles and allied topics, and the elements of inversion.
Contents
The foundation of euclidean geometry
The fifth postulate
The discovery of non-euclidean geometry
Hyperbolic plane geometry
Hyperbolic plane trigonometry
Applications of calculus to the solutions of some problems in hyperbolic geometry
Elliptic plane geometry and trigonometry
The consistency of the non-euclidean geometries