Euclid's Parallel Postulate: Its Nature, Validity and Place in Geometrical Systems
by John William Withers
Publisher: Open Court Publishing Co. 1904
Number of pages: 214
The parallel postulate is the only distinctive characteristic of Euclid. To pronounce upon its validity and general philosophical significance without endeavoring to know what Non-Euclideans have done would be an inexcusable blunder. For this reason I have given in the following pages what might otherwise seem to be an undue prominence to the historical aspect of my general problem.
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by Mike Hitchman
This text develops non-Euclidean geometry and geometry on surfaces at a level appropriate for undergraduate students who completed a multivariable calculus course and are ready to practice habits of thought needed in advanced undergraduate courses.
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These notes are intended as a relatively quick introduction to hyperbolic geometry. They review the wonderful history of non-Euclidean geometry. They develop a number of the properties that are particularly important in topology and group theory.
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Examines various attempts to prove Euclid's parallel postulate - by the Greeks, Arabs and Renaissance mathematicians. It considers forerunners and founders such as Saccheri, Lambert, Legendre, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky.