Chapter XII. Three Classical Geometrical Problems.

Statement of the Problems 284
The Duplication of the Cube. Legendary Origin of the Problem . . 285
Hippocrates's Lemma 287
Solutions by Archytas, Plato, Menaechmus, Apollonius, and Diodes . 287 Solutions by Vieta, Descartes, Gregory of St Vincent, and Newton
The Trisection of an Angle
Ancient Solutions quoted by Pappus
Solutions by Pappus, Descartes, Newton, Clairaut, and
The Quadrature of the Circle .....
Incommensurability of tt
Definitions of tt
Origin of symbol tt
Methods of approximating to the numerical value of ir Geometrical methods of Approximation .
Eesults of Egyptians, Babylonians, Jews
Eesults of Archimedes and other Greek Writers
Eesults of Eoman Surveyors and Gerbert
Eesults of Indian and Eastern Writers
Eesults of European Writers, 1200-1630 Theorems of Wallis and Brouncker Analytical methods of Approximation. Gregory's series
Eesults of European Writers, 1699-1873
Geometrical Approximation
Approximations by the Theory of Probability
290 291 291 292 293 294 295 296 296 296 297 297 298 298 300 302 303 303 305 305