Ⅰ Intersections of Curves 1
Introduction and History 1
1. Intersections at the Origin 4
2. Homogeneous Coordinates 17
3. Intersections in Homogeneous Coordinates 31
4. Lines and Tangents 50
Ⅱ Conics 69
Introduction and History 69
5. Conics and Intersections 73
6. Pascal's Theorem 92
7. Envelopes of Conics 110
Ⅲ Cubics 127
Introduction and History 127
8. Flexes and Singular Points 134
9. Addition on Cubics 153
10. Complex Numbers 175
11. Bezout's Theorem 195
12. Hessians 211
13. Determining Cubics 229
Ⅳ Parametrizing Curves 245
Introduction and History 245
14.Parametrizations at the Origin 249
15.Parametrizations of General Form 276
16.Envelopes of Curves 304
References 340
Index 343