总目录

Vol I. An Axiomatic Approach to Geometry


1. Pre-Hellenic Antiquity
2. Some Pioneers of Greek Geometry
3. Euclid's Elements
4. Some Masters of Greek Geometry
5. Post-Hellenic Euclidean Geometry
6. Projective Geometry
7. Non-Euclidean Geometry
8. Hilbert's Axiomatization of the Plane

Appendices
A. Constructibility
B. The Three Classical Problems
C. Regular Polygons

Vol II. An Algebraic Approach to Geometry

1. The Birth of Analytic Geometry
2. Affine Geometry
3. More on Real Affine Spaces
4. Euclidean Geometry
5. Hermitian Spaces
6. Projective Geometry
7. Algebraic Curves

Appendices
A. Polynomials over a Field
B. Polynomials in Several Variables
C. Homogeneous Polynomials
D. Resultants
E. Symmetric Polynomials
F. Complex Numbers
G. Quadratic Forms
H. Dual Spaces

Vol III. A Differential Approach to Geometry

1. The Genesis of Differential Methods
2. Plane Curves
3. A Museum of Curves
4. Skew Curves
5. The Local Theory of Surfaces
6. Towards Riemannian Geometry
7. Elements of the Global Theory of Surfaces

Appendices
A. Topology
B. Differential Equations

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