The Foundations of Geometry (Classic Reprint)
by Edward Travers Dixon (9781330281345)

The Foundations of Geometry (Classic Reprint)
 
Edward Travers Dixon
Format: Paperback / softback
Pages: 156
Category: Geometry
Publisher: Forgotten Books
ISBN: 9781330281345
ISBN-10: 1330281349



Excerpt from The Foundations of Geometry (Whether you think these properties me established by Euclid's geometry, or not, is immaterial. If you giant this you have granted my Axiom II.; for this does not assert any objective fact at all.) (iv) Do you accept the logical accuracy and permissibility of my remaining definitions and axioms? (Objections on the score of convenience and simplicity had better be considered elsewhere.) (v) Do you admit the formal accuracy of the proofs of propositions in my Books I. and II.? (N.B. If you admit this there can no longer be any doubt as to the sufficiency of my premises.) (vi) Do you admit the objective applications of my three Axioms, and therefore of my system of geometry, as discussed in Chap. I. of Part. III.? (vii) If you admit that there is a theoretical doubt as to the objective counterpart of my second Axiom, please give any criticisms which may occur to you on the remainder of Part III. Now, if there is no flaw in the line of argument I have adopted, it follows that my conclusions arc time, and consequently that any objection taken to them outside this line of argument, however specious it may sound, must contain a fallacy. I might therefore refuse to discuss such an objection. But the objector might truly urge that, conversely, if his objection was irrefutable, there must be some hidden fallacy in my argument. And therefore, though I prefer arguing in my own way, having devoted a good deal of thought to the subject, and having come to the conclusion that my line of argument is the most direct, and the easiest to discuss; I shall nevertheless feel bound to give the best answer I can to any reasonable objection whatever. 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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