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.
