Principles of Geometry: Vol. 2. Plane GeometryCUP 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 |
243 | |
245 | |
Common terms and phrases
a₁ adjoint curves aggregate algebraic curve algebraic integral arbitrary point b₁ branch place C₂ canonical curve canonical series coefficients coincident complete intersection conic consider constant coordinates coresidual corresponding cubic curve cubic surface curve C₁ curve in space curve of order cusp definite denote determinant dimensions double points equation everywhere finite integrals expression formula freedom g₁ genus given curve hence homogeneous infinity inflexion integral functions irreducible k₁ linear series linearly independent matrix meet the curve multiple points n₁ neighbourhood obtained order n-3 original curve osculating plane oval cut p₁ parameter pass plane curve points of F=0 poles polynomial power series primals of order prime proved quadric surface quartic quintic curve rational function Riemann surface rows ruled surface series g series of sets sextic curve shewn space curve suppose surfaces of order tangent line theorem u₁ vanishes variable zero