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 Barycenters
2.9 Barycentric Coordinates
2.10 Triangles
2.11 Parallelograms
2.12 Affine Transformations
2.13 Affine Isomorphisms
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 of a Quadric
2.26 The Equation of a Non-degenerate Quadric
2.27 Problems
2.28 Exercises
3 More on Real Affine Spaces
3.1 About Left, Right and Between
3.2 Orientation of a Real Affine Space
