Introductory Non-Euclidean Geometry

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Format: Paperback
Pub. Date: 2005-02-18
Publisher(s): Dover Publications
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Summary

This versatile introduction to non-Euclidean geometry is appropriate for both high-school and college classes. The first two-thirds of the book requires a familiarity with plane and solid geometry and trigonometry, with calculus employed only in the final part.

Table of Contents

INTRODUCTION
CHAPTER I PANGEOMETRY 1(30)
I. PROPOSITIONS DEPENDING ONLY ON THE PRINCIPLE OF SUPERPOSITION
3(3)
II. PROPOSITIONS WHICH ARE TRUE FOR RESTRICTED FIGURES
6(5)
III. THE THREE HYPOTHESES
11(20)
CHAPTER II THE HYPERBOLIC GEOMETRY
I. PARALLEL LINES
31(12)
II. BOUNDARY-CURVES AND SURFACES, AND EQUIDISTANT-CURVES AND SURFACES
43(10)
III. TRIGONOMETRICAL FORMULÆ
53(9)
CHAPTER III THE ELLIPTIC GEOMETRY 62(7)
CHAPTER IV ANALYTIC NON-EUCLIDEAN GEOMETRY
I. HYPERBOLIC ANALYTIC GEOMETRY
69(11)
II. ELLIPTIC ANALYTIC GEOMETRY
80(6)
III. ELLIPTIC SOLID ANALYTIC GEOMETRY
86(5)
HISTORICAL NOTE 91

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