## Geometry Without Axioms; Or the First Book of Euclid's Elements: With Alterations and Familiar Notes; And an Intercalary Book in Which the Straight Line and Plane Are Derived from Properties of the Sphere; Being an Attempt to Get Rid of Axioms and PostulaGilbert Fred Richard J R Timothy Gilbert Gilbert Fred J R Timothy Fred J R Timothy Gilbert Gilbert Thompson Thompson, Thompson Thompson Fb&c Limited, 4. jun. 2017 - 164 sider Excerpt from Geometry Without Axioms; Or the First Book of Euclid's Elements: With Alterations and Familiar Notes; And an Intercalary Book in Which the Straight Line and Plane Are Derived From Properties of the Sphere; Being an Attempt to Get Rid of Axioms and Postulates; And Particularly to Establish the Theory of Parallel Lines W XXVIII D in the First Book, where the conclusion rests entirely on the impossibility of a certain line ceasing to cut a series of other lines during a continuous motion, in a way incapable of being supplied by any succession of insulated positions as like wise in part of Prop. XII Cor. 8 of the Intercalary Book, and else where. On the whole therefore it may be an interesting question in what place a geometer would be warranted in saying, I could have proved these preliminaries, but it would have been necessary to disturb the order which directs that lines be treated of first and solids afterwards, and to introduce motion; for which reason it was considered better that they should be adopted without proof.' 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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