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Inhaltsangabe
Excerpt from Non-Euclidean Geometry
The axioms of Geometry were formerly regarded as laws of thought which an intelligent mind could neither deny nor investigate. Not only were the axioms to which we have been accustomed found to agree with our experience, but it was believed that we could not reason on the supposition that-any of them are not true. It has been Shown, however, that it is possible to take a set of axioms, wholly or in part contradicting those of Euclid, and build up a Geometry as consistent as his.
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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 state of such historical works.
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Reseña del editor
Excerpt from Non-Euclidean Geometry
The axioms of Geometry were formerly regarded as laws of thought which an intelligent mind could neither deny nor investigate. Not only were the axioms to which we have been accustomed found to agree with our experience, but it was believed that we could not reason on the supposition that-any of them are not true. It has been Shown, however, that it is possible to take a set of axioms, wholly or in part contradicting those of Euclid, and build up a Geometry as consistent as his.
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 state of such historical works.
Reseña del editor
Excerpt from Non-Euclidean Geometry
Non-Euclidean Geometry is now recognized as an important branch of Mathematics. Those who teach Geometry should have some knowledge of this subject, and all who are interested in Mathematics will find much to stimulate them and much for them to enjoy in the novel results and views that it presents.
This book is an attempt to give a simple and direct account of the Non-Euclidean Geometry, and one which presupposes but little knowledge of Mathematics. The first three chapters assume a knowledge of only Plane and Solid Geometry and Trigonometry, and the entire book can be read by one who has taken the mathematical courses commonly given in our colleges.
No special claim to originality can be made for what is published here. The propositions have long been established, and in various ways. Some of the proofs may be new, but others, as already given by writers on this subject, could not be improved. These have come to me chiefly through the translations of Professor George Bruce Halsted of the University of Texas.
I am particularly indebted to my friend, Arnold B. Chace, Sc. D., of Valley Falls, R. I., with whom I have studied and discussed the subject.
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 state of such historical works.
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NonEuclidean Geometry Classic Reprint
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NonEuclidean Geometry Classic Reprint
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Non-Euclidean Geometry (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. In a world of different geometries, this book explores a geometry discovered by Lobachevsky, where lines that don't intersect continually approach each other. Unlike familiar Euclidean geometry, this Hyperbolic Geometry presents a fascinating universe where the sum of a triangle's angles is less than 180 degrees and parallel lines diverge as they extend infinitely. With detailed exploration of its intriguing concepts through propositions, theorems, and analytical methods, the author reveals the unique properties of this non-Euclidean realm. By comparing it with Euclidean and Elliptic Geometries, the book offers a profound insight into the nature of geometry itself. 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. print-on-demand item. Bestandsnummer des Verkäufers 9781330266373_0
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