Chapters in this book

1. Frontmatter i
2. Contents vii
3. Preface xi
4. Introduction 1
5. CHAPTER 1. The Four Problems 7
6. CHAPTER 1. The Four Problems 25
7. CHAPTER 3. Compass-and- Straightedge Constructions 38
8. CHAPTER 4. The First Mathematical Crisis 56
9. CHAPTER 5. Doubling the Cube 69
10. CHAPTER 6. The Early History of π 81
11. CHAPTER 7. Quadratures 95
12. CHAPTER 8. Archimedes’s Number 108
13. CHAPTER 9. The Heptagon, the Nonagon, and the Other Regular Polygons 137
14. CHAPTER 10. Neusis Constructions 146
15. CHAPTER 11. Curves 160
16. CHAPTER 12. Getting By with Less 178
17. CHAPTER 13. The Dawn of Algebra 196
18. CHAPTER 14. Viète’s Analytic Art 219
19. CHAPTER 15. Descartes’s Compass-and- Straightedge Arithmetic 233
20. CHAPTER 16. Descartes and the Problems of Antiquity 254
21. CHAPTER 17. Seventeenth- Century Quadratures of the Circle 268
22. CHAPTER 18. Complex Numbers 288
23. CHAPTER 19. Gauss’s 17-gon 302
24. CHAPTER 20. Pierre Wantzel 320
25. CHAPTER 21. Irrational and Transcendental Numbers 348
26. EPILOGUE. Sirens or Muses? 367
27. Notes 369
28. References 405
29. Index 429