Book contents
- Frontmatter
- PREFACE
- Contents
- CHAPTER I INTRODUCTORY. RELATIONS OF THE GEOMETRY OF TWO, THREE, FOUR AND FIVE DIMENSIONS
- CHAPTER II HART'S THEOREM, FOR CIRCLES IN A PLANE, OR FOR SECTIONS OF A QUADRIC
- CHAPTER III THE PLANE QUARTIC CURVE WITH TWO DOUBLE POINTS
- CHAPTER IV A PARTICULAR FIGURE IN SPACE OF FOUR DIMENSIONS
- CHAPTER V A FIGURE OF FIFTEEN LINES AND POINTS, IN SPACE OF FOUR DIMENSIONS; AND ASSOCIATED LOCI
- CHAPTER VI A QUARTIC SURFACE IN SPACE OF FOUR DIMENSIONS. THE CYCLIDE
- CHAPTER VII RELATIONS IN SPACE OF FIVE DIMENSIONS. KUMMER'S SURFACE
- CORRECTIONS TO VOLUME III
- INDEX
- Frontmatter
- PREFACE
- Contents
- CHAPTER I INTRODUCTORY. RELATIONS OF THE GEOMETRY OF TWO, THREE, FOUR AND FIVE DIMENSIONS
- CHAPTER II HART'S THEOREM, FOR CIRCLES IN A PLANE, OR FOR SECTIONS OF A QUADRIC
- CHAPTER III THE PLANE QUARTIC CURVE WITH TWO DOUBLE POINTS
- CHAPTER IV A PARTICULAR FIGURE IN SPACE OF FOUR DIMENSIONS
- CHAPTER V A FIGURE OF FIFTEEN LINES AND POINTS, IN SPACE OF FOUR DIMENSIONS; AND ASSOCIATED LOCI
- CHAPTER VI A QUARTIC SURFACE IN SPACE OF FOUR DIMENSIONS. THE CYCLIDE
- CHAPTER VII RELATIONS IN SPACE OF FIVE DIMENSIONS. KUMMER'S SURFACE
- CORRECTIONS TO VOLUME III
- INDEX
Summary
The present volume, the first written and the most revised, of the book, for which indeed, mostly, the earlier volumes were undertaken, still bears many marks of the difficulty of compressing the matter into brief compass. But the writer hopes that it may seem to the reader as remarkable as it does to him, that it should be possible to comprehend under one point of view, and that so simple, the introduction to nearly all the surfaces ordinarily studied in the geometry of three dimensions, as well as the usual line geometry. Chapters V, VI, VII seek to make clear that this is so. To these the earlier chapters are auxiliary. But Chapters II and IV have been introduced as much for their own interest as for their illustrative value; the results obtained in these two chapters are not required in the subsequent pages. It is hoped that the Table of Contents, and the Index, may make it easy to use the volume. It will of course be understood that the volume is throughout intended to be introductory and illustrative; hardly anywhere is it complete.
To the Staff of the University Press grateful acknowledgments are due for their continued courtesy and care.
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- Principles of Geometry , pp. vii - viiiPublisher: Cambridge University PressPrint publication year: 2010First published in: 1925