비 유클리드 기하학 (Non -Euclidean Geometry, by HenryManning)

비 유클리드 기하학. Non -Euclidean Geometry ,byHenryManning
Contents
PREFACE ii
1 INTRODUCTION 1
2 PANGEOMETRY 3
2.1 Propositions Depending Only on the Principle of Superposition . 3
2.2 Propositions Which Are True for Restricted Figures . . . . . . . 6
2.3 The Three Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . 9
3 THE HYPERBOLIC GEOMETRY 25
3.1 Parallel Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Boundary-curves and Surfaces, and Equidistant-curves and Surfaces 35
3.3 Trigonometrical Formulæ . . . . . . . . . . . . . . . . . . . . . . 42
4 THE ELLIPTIC GEOMETRY 51
5 ANALYTIC NON-EUCLIDEAN GEOMETRY 56
5.1 Hyperbolic Analytic Geometry . . . . . . . . . . . . . . . . . . . 56
5.2 Elliptic Analytic Geometry . . . . . . . . . . . . . . . . . . . . . 68
5.3 Elliptic Solid Analytic Geometry . . . . . . . . . . . . . . . . . . 74
6 HISTORICAL NOTE 79