Principles of Geometry
6 Volume Paperback Set

Table of Contents

Volume 1: Preface
Introductory
1. Abstract geometry
2. Real geometry
3. Abstract geometry, resumed
Bibliographical
Index. Volume 2: Preface
Preliminary
1. General properties of conics
2. Properties relative to two points of reference
3. The equation of a line, and of a conic
4. Restriction of the algebraic symbols. The distinction of real and imaginary elements
5. Properties relative to an absolute conic. The notion of distance. Non-Euclidean geometry
Notes
Index. Volume 3: Preface
1. Introduction to the theory of quadric surfaces
2. Relations with a fixed conic. Spheres, confocal surfaces: quadrics through the intersection of two general quadrics
3. Cubic curves in space. The intersection of two or more quadrics
4. The general cubic surface: introductory theorems
Corrections for volumes 1 and 2
Index. Volume 4: Preface
1. Introductory. Relations of the geometry of two, three, four and five dimensions
2. Hart's theorem, for circles in a plane, or for sections of a quadric
3. The plane quartic curve with two double points
4. A particular figure in space of four dimensions
5. A figure of fifteen lines and points, in space of four dimensions and associated loci
6. A quartic surface in space of four dimensions. The cyclide
7. Relations in space of five dimensions. Kummer's surface
Corrections to volume 3
Index. Volume 5: Preface
1. Introductory account of rational and elliptic curves
2. The elimination of the multiple points of a plane curve
3. The branches of an algebraic curve. The order of a rational function. Abel's theorem
4. The genus of a curve. Fundamentals of the theory of linear series
5. The periods of algebraic integrals. Loops in a plane. Riemann surfaces
6. The various kinds of algebraic integrals. Relations among periods
7. The modular expression of rational functions and integrals
8. Enumerative properties of curves
Index. Volume 6: Preface
1. Algebraic correspondence
2. Schubert's calculus. Multiple correspondence
3. Transformations and involutions for the most part in a plane
4. Preliminary properties of surfaces in three and four dimensions
5. Introduction to the theory of the invariants of birational transformation of a surface, particularly in space of three dimensions
6. Surfaces and primals in four dimensions. Formulae for intersections
7. Illustrative examples and particular theorems
Index.