TAILIEUCHUNG - The Project Gutenberg EBook of The Elements of non-Euclidean Geometry, by Julian Lowell Coolidge 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

The Project Gutenberg EBook of The Elements of non-Euclidean Geometry, by Julian Lowell Coolidge 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 Title: The Elements of non-Euclidean Geometry Author: Julian Lowell Coolidge Release Date: August 20, 2008 [EBook #26373] Language: English 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. | The Project Gutenberg EBook of The Elements of non-Euclidean Geometry by Julian Lowell Coolidge 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 Title The Elements of non-Euclidean Geometry Author Julian Lowell Coolidge Release Date August 20 2008 EBook 26373 Language English 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 THE ELEMENTS OF NON-EUCLIDEAN GEOMETRY BY JULIAN LOWELL COOLIDGE . 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. In this as in all other changes there is subject both for rejoicing and regret. It is a satisfaction to a writer on non-euclidean geometry that he may proceed at once to his subject without feeling any need to justify himself or at least any more need than any other who adds to our supply of books. On the other hand he will miss the stimulus that comes to one who feels that he is bringing out something entirely new and strange. The subject of non-euclidean geometry is to the mathematician quite as well established as any other branch of mathematical science and in fact it may lay claim to a decidedly more .

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