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本附件包括：- Francis Borceux-A Differential Approach to Geometry_ Geometric Trilogy_3.pdf
- Francis Borceux-A Differential Approach to Geometry_ Geometric Trilogy_1.pdf
- Francis Borceux-A Differential Approach to Geometry_ Geometric Trilogy_2.pdf
An Axiomatic Approach to Geometry Geometric Trilogy I
几何三部曲 第1卷：几何的公理化方法
An Algebraic Approach to Geometry Geometric Trilogy II
几何三部曲 第2卷：几何的代数方法
A Differential Approach to Geometry Geometric Trilogy III
几何三部曲 第3卷：几何的微分方法
本书以几何公理化方法的历史发展成果为基础，系统给出了欧几里得几何、非欧几里得几何和投影几何研究的现代方法。公理化几何是形式化数学的起源，其中有很多著名问题有待解决。对这些著名问题的研究往往会导致许多研究领域特别是代数研究领域的产生。基于公理化思想的数学理论是现代数学的基本特征。本书详尽地论述了公理化几何研究的内容，也给出了许多著名问题的完备性证明。
Francis Borceux，是一位比利时数学家。他的巨著《几何三部曲》，非常适合从事数学史、几何学、代数及其相关领域研究生和科研人员阅读和参考。
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
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
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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