Squaring The Circle And Other MonographsPDF电子书下载

CHAPTER Ⅰ GENERAL ACCOUNT OF THE PROBLEM 1

CHAPTER Ⅱ THE FIRST PERIOD 13

CHAPTER Ⅲ THE SECOND PERIOD 36

CHAPTER Ⅳ THE THIRD PERIOD 43

Ⅰ．INTRODUCTION 65

Ⅱ．POSSIBLE CONSTRUCTIONS 72

Ⅲ．RULER CONSTRUCTIONS 99

Ⅳ．RULER AND COMPASS CONSTRUCTIONS 123

Ⅴ．STANDARD METHODS 142

Ⅵ．COMPARISON OF METHODS 165

Ⅶ．ONE FIXED CIRCLE 182

Ⅷ．COMPASSES ONLY 195

FIRST LECTURE FUNCTIONS DEFINED BY SERIES 219

1．Early notions 219

2．Early history of the calculus 220

3．The calculus in India 221

4．Continuity and differentiability 222

5．Riemann＇s non-differentiable function 223

6．Condensation of singularities 224

7．Weierstrase＇s discovery 224

8．Attempts of other writers 225

9．Bolzano＇s function 225

10．The effect of Weierstrass＇s discovery 226

11．Work relating to Weirstrass＇s function 227

12．The series definition 229

13．Dini＇s method 230

14．Proof of Weierstrass＇s result 235

15．Non-existence of the derivative 237

16．Some important non-differentiable functions defined byseries 239

SECOND LECTURE FUNCTIONS DEFINED GEOMETRICALLY 242

1．Bolzano＇s curve 242

2．Koch＇s curve 247