The Elements of Non-Euclidean Geometry (Classic Reprint)

Julian Lowell Coolidge

ISBN 10: 1330306767 / ISBN 13: 9781330306765

Published by Forgotten Books, 2018

About this Item

Print on Demand. This book takes a deep dive into the fascinating world of non-Euclidean geometry. The author explores the foundations of this area of mathematics, which challenges the traditional axioms of Euclid, and traces its evolution from a once controversial subject to a well-established field of study. The book delves into the key concepts, including the three main hypotheses of non-Euclidean geometry, the trigonometric and analytic formulae that define these systems, and the various geometric objects within them, such as circles, spheres, and conic sections. It also examines the consistency and significance of the axioms that underpin this field, and explores the relationship between non-Euclidean geometry and other branches of mathematics, such as projective geometry and differential geometry. The author presents the different approaches to understanding and applying non-Euclidean geometry, making this book a comprehensive resource for anyone interested in exploring the intriguing complexities and applications of this powerful field. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. Seller Inventory # 9781330306765_0

Bibliographic Details

Title: The Elements of Non-Euclidean Geometry (...

Publisher: Forgotten Books

Publication Date: 2018

Binding: Paperback

Condition: New

Book Type: print-on-demand item

About this title

Synopsis:

Excerpt from The Elements of Non-Euclidean Geometry The heroic age of non-euclidean geometry is passed. It is long since the days when Lobachevsky 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 now 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. Recent books dealing with non-euclidean geometry fall naturally into two classes. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the stat