Chapter XIII. The Parallel Postulate

The Problem .... The Earliest Proof. Thales . Pascal's Proof .... Pythagorean and Euclidean Proof Features of the Problem . Ptolemy's Proof of the Postulate Proclus's Proof of the Postulate Wallis's Proof of the Postulate Bertrand's Proof of the Postulate
307 308 308 310 311 313 314 314 315
TABLE OF CONTENTS
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Playfair's Proof of the Postulate 316
Playfair's Rotational Proof of the Proposition 317
Legendre's First Proof of the Proposition ...... 318
Legendre's Analytical Proof of the Proposition 318
Lagrange's Memoir ........... 320
Other Parallel Postulates 320
Definitions of Parallels .......... 322
Non-Euclidean Systems 323
Comparison of Elliptic, Parabolic and Hyperbolic Geometries . 325