The Theory of the Imaginary in Geometry: Together With the Trigonometry of the Imaginary (Classic Reprint) - Softcover

Hatton, J. L. S.

9781330051078: The Theory of the Imaginary in Geometry: Together With the Trigonometry of the Imaginary (Classic Reprint)

Softcover

ISBN 10: 1330051076 ISBN 13: 9781330051078

Verlag: Forgotten Books, 2019

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Excerpt from The Theory of the Imaginary in Geometry: Together With the Trigonometry of the Imaginary

To Professor Whitehead, the author has to tender his sincerest thanks for much valuable help and assistance. To Professor gts. Le Beau and Mr S. G. Soal of the. East London College he is indebted for very valuable advice and criticism. To Mr J. B. Peace of the Cambridge Univers1ty Press he desires to tender his warmest thanks for the great assistance which he has rendered in connection with this book.

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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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Excerpt from The Theory of the Imaginary in Geometry: Together With the Trigonometry of the Imaginary

The position of any real point in space may be determined by means of three real coordinates, and any three real quantities may be regarded as determining the position of such a point In Geometry as in other branches of Pure Mathematics the question naturally arises, whether the quantities concerned need necessarily be real. Such a Geometry contains as a particular case the Geometry of real points. The relationship of the more generalised conception of Geometry and of space to the particular case of real Geometry is of importance, as points, whose determining elements are complex quantities, arise both in coordinate and in projective Geometry.

In this book an attempt has been made to work out and determine this relationship. Either of two methods might have been adopted. It would have been possible to lay down certain axioms and premises and to have developed a general theory therefrom. This has been done by other authors. The alternative method, which has been employed here, is to add to the axioms of real Geometry certain additional assumptions. From these, by means of the methods and principles of real Geometry, an extension of the existing ideas and conception of Geometry can be obtained. In this way the reader is able to approach the simpler and more concrete theorems in the first instance, and step by step the well-known theorems are extended and generalised. A conception of the imaginary is thus gradually built up and the relationship between the imaginary and the real is exemplified and developed.

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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