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1. HISTORICAL. 2. ELEMENTARY HYPERBOLIC GEOMETRY. 3. ELLIPTIC GEOMETRY. 4. ANALYTICAL GEOMETRY. 5. REPRESENTATIONS OF NON-EUCLIDEAN GEOMETRY IN EUCLIDEAN SPACE. 6. "SPACE-CURVATURE" AND THE PHILOSOPHICAL BEARING OF NON-EUCLIDEAN GEOMETRY. 7. RADICAL AXES, HOMOTHETIC CENTRES, AND SYSTEMS OF CIRCLES. 8. INVERSION AND ALLIED TRANSFORMATIONS 9. THE CONIC.
This is a well-known book that introduces readers to the fascinating world of non-Euclidean geometry which is now a well-recognised branch of mathematics. It is the general type of geometry of homogeneous and continuous space, of which euclidean geometry is a special form. This book talks about two main types called hyperbolic and elliptic geometry. It uses easy words and examples to help people understand these new ideas about shapes and space. It is good for students and anyone who wants to learn about geometry beyond the usual kind. This text treats such important and difficult topics as the relation between parataxy and parallelism, the absolute measure, the pseudosphere, Gauss’ proof of the defect-area theorem, geodesic representation, and other advanced subjects. In addition, its 136 problems offer practice in using the forms and methods developed in the text.
Title: The Elements of Non-Euclidean Geometry by D.M.Y. Sommerville Publisher: G. Bell & Sons Ltd Year: 1914 Pages: 301 Type: PDF Language: English ISBN-10 #: 1017414920 ISBN-13 #: 978-1017414929 License: Public Domain Work Amazon: Amazon
The author Duncan MacLaren Young Sommerville was a Scottish mathematician and astronomer. He was well knwon for his work on Non-Euclidean Geometry. He taught math in Scotland and New Zealand. He wrote important books to help students understand new ideas in geometry. He also liked painting and helped start the New Zealand Astronomical Society. He was honored for his work and joined the Royal Society of Edinburgh.
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