Principles of Geometry, Volumes 1-3

Front Cover
CUP Archive, 1922 - Geometry - 182 pages
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 second volume, describes the principal configurations of space of two dimensions.
 

Contents

INTRODUCTORY ACCOUNT
1
Greatest possible number of double points of a plane curve 1011
10
Examples of elliptic curves Coresiduation Salmons
18
THE ELIMINATION OF THE MULTIPLE
24
Examples of transformation of curves 3134
31
The parametric expression of a branch of a curve 3943
39
General theorem for infinities of a rational function 4649
46
Examples of Abels theorem 5557
55
Riemann surfaces
121
INTEGRALS RELATIONS AMONG PERIODS
136
Modular expression of a rational function
147
A significant matrix identity
157
The structure of a certain fundamental rational function
169
Some particular applications Return to theory of special
176
Examples Composite curve intersection of two surfaces
178
General formulae connecting characteristics of a curve
182

MENTALS OF THE THEORY OF LINEAR SERIES
59
Equivalent or coresidual sets of points on the curve
65
Applications of the RiemannRoch formula
78
The existence of a rational function with assigned poles
86
Examples of existing special series
99
Related theorem as to intersections of plane curves
107
The method of loops in a plane
113
Curves which are the complete intersection of two surfaces
201
Curves which are the partial intersection of two surfaces
208
Linear series upon a curve in space
215
Another proof of the determination of the canonical series
226
Examples for cases of composite intersections
234
PAGES
243

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