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Excerpt from Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical Systems: Thesis Presented to the Philosophical Faculty of Yale University for the Degree of Doctor of Philosophy I have included in the bibliography such works as are mentioned in the body of the thesis, and have not aimed at making a complete list. More complete biographies of Hyperspace and non Euclidean Geometry are those of Halsted and Bon ola, which I have mentioned in my list. 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.