Principles of Geometry

H. F. Baker

doi:10.1017/CBO9780511718311

Henry Frederick Baker (1866–1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the sixth and final volume, describes the birational geometric theory of surfaces.

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Principles of Geometry

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Contents

Frontmatter
pp i-viii

PREFACE
pp ix-x

Contents
pp xi-xiv

CHAPTER I - ALGEBRAIC CORRESPONDENCE
pp 1-68

CHAPTER II - SCHUBERT'S CALCULUS. MULTIPLE CORRESPONDENCE
pp 69-111

CHAPTER III - TRANSFORMATIONS AND INVOLUTIONS FOR THE MOST PART IN A PLANE
pp 112-147

CHAPTER IV - PRELIMINARY PROPERTIES OF SURFACES IN THREE AND FOUR DIMENSIONS
pp 148-181

CHAPTER V - INTRODUCTION TO THE THEORY OF THE INVARIANTS OF BIRATIONAL TRANSFORMATION OF A SURFACE, PARTICULARLY IN SPACE OF THREE DIMENSIONS
pp 182-241

CHAPTER VI - SURFACES AND PRIMALS IN FOUR DIMENSIONS. FORMULAE FOR INTERSECTIONS
pp 242-270

CHAPTER VII - ILLUSTRATIVE EXAMPLES AND PARTICULAR THEOREMS
pp 271-300

INDEX
pp 301-308

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