二次曲线和三次曲线 原书第2版 英文PDF电子书下载

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