Principles of Geometry: Vol. 2. Plane Geometry

Front Cover
CUP Archive, 1954 - 259 pages
 

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
THE MODULAR EXPRESSION
147
Important properties of the fundamental integral functions 151155
157
The structure of a certain fundamental rational function
169
ENUMERATIVE PROPERTIES
182
Curves which are the complete intersection of two surfaces
201
Curves which are the partial intersection of two surfaces
208

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
The theory of special sets an extension of Cliffords theorem
94
Canonical forms for the equation of a manifold or several
107
The method of loops in a plane
113
Examples Curves not determinable by three surfaces
209
Examples Composite curve intersection of two surfaces
216
Another proof of the determination of the canonical series
226
The greatest genus possible for a curve of given order
234
Examples The form of the everywhere finite integrals
243
Curve systems on a surface The EulerPoincaré invariant
245

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