Geometric trilogy:Ó¢ÎÄ:¢ò:An algebraic approach to geometry

1 The Birth of Analytic Geometry
1£®1 Fermat's Analytic Geometry
1£®2 Descartes' Analytic Geometry
1£®3 More on Cartesian Systems of Coordinates
1£®4 Non-Cartesian Systems of Coordinates
1£®5 Computing Distances and Angles
1£®6 Planes and Lines in Solid Geometry
1£®7 The Cross Product
1£®8 Forgetting the Origin
1£®9 The Tangent to a Curve
1£®10 The Conics
1£®11 The Ellipse
1£®12 The Hyperbola
1£®13 The Parabola
1£®14 The Quadrics
1£®15 The Ruled Quadrics
1£®16 Problems
1£®17 Exercises

2 Affine Geometry
2£®1 Affine Spaces over a Field
2£®2 Examples of Affine Spaces
2£®3 Affine Subspaces
2£®4 Parallel Subspaces
2£®5 Generated Subspaces
2£®6 Supplementary Subspaces
2£®7 Lines and Planes
2£®8 Bary centers
2£®9 Bary centric Coordinates
2£®10 Triangles
2£®11 Parallelograms
2£¬12 Affine Transformations
2£®13 Affine Isomorphism
2£®14 Translations
2£®15 Projections
2£®16 Symmetries
2£®17 Homotheties and Affinities
2£®18 The Intercept Thales Theorem
2£®19 Affine Coordinates
2£®20 Change of Coordinates
2£®21 The Equations of a Subspace
2£®22 The Matrix of an Affine Transformation
2£®23 The Quadrics
2£®24 The Reduced Equation of a Quadric
2£®25 The Symmetries ofa Quadric
2£®26 The Equation of a Non-degenerate Quadric
2£®27 Problems
2£®28 Exercises
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3 More on Real Affine Spaces
4 Euclidean Geometry
5 Hermitian Spaces
6 Projective Geometry
7 Algebraic Curves

Appendix
References and Furtber Reading
Index