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THE ELEMENTS OF NON-EUCLIDEAN GEOMETRY

JULIAN LOWELL COOLIDGE Ph.D.

ASSISTANT PROFESSOR OF MATHEMATICS

IN HARVARD UNIVERSITY



FIRST PRESS: OXFORD AT THE CLARENDON PRESS, 1909


All rights reserved. No part of this publication may be reproduced or

transmitted, in any form or by any means, without permission. Any

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be liable for criminal prosecution and civil claims for damages.

Published by:

GLOBAL ACADEMY, 2014

Language: English

E-mail: globalyayinlari@gmail.com

Website: https://www.globalacademy.com.tr


PERFACE

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 solid

basis than some branches, such as the theory of assemblages, or the analysis

situs.




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