The Elements of non-Euclidean Geometry

The Project Gutenberg EBook of The Elements of Julian Lowell Coolidge non-Euclidean Geometry, by This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever.You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: The Elements of non-Euclidean Geometry Author: Julian Lowell Coolidge Release Date: August 20, Language: English 2008 [EBook #26373] Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK NON-EUCLIDEAN GEOMETRY *** Produced by Joshua Hutchinson, David Starner, Keith Edkins and the Online Distributed Proofreading Team at http://www.pgdp.net THE ELEMENTS OF NON-EUCLIDEAN GEOMETRY BY JULIAN LOWELL COOLIDGE Ph.D. ASSISTANT PROFESSOR OF MATHEMATICS IN HARVARD UNIVERSITY OXFORD AT THE CLARENDON PRESS 1909 PREFACE The heroic age of non-euclidean geometry is passed.It is long since the days when Lobatchewsky timidly referred to his system as an ‘imaginary geometry’, and the new subject appeared as a dangerous lapse from the orthodox doctrine of Euclid.The attempt to prove the parallel axiom by means of the other usual assumptions is now seldom undertaken, and those who do undertake it, are considered in the class with circle-squarers and searchers for perpetual motion– sad by-products of the creative activity of modern science.