Julian Lowell Coolidge

The Elements of Non-Euclidean Geometry Julian Lowell Coolidge

CHAPTER I FOUNDATION FOR METRICAL GEOMETRY IN A LIMITED REGION

CHAPTER II CONGRUENT TRANSFORMATIONS

CHAPTER III THE THREE HYPOTHESES

CHAPTER IV THE INTRODUCTION OF TRIGONOMETRIC FORMULAE

CHAPTER V ANALYTIC FORMULAE

CHAPTER VI CONSISTENCY AND SIGNIFICANCE OF THE AXIOMS

CHAPTER VII THE GEOMETRIC AND ANALYTIC EXTENSION OF SPACE

CHAPTER VIII THE GROUPS OF CONGRUENT TRANSFORMATIONS

CHAPTER IX POINT, LINE, AND PLANE TREATED ANALYTICALLY

CHAPTER X THE HIGHER LINE GEOMETRY

CHAPTER XI THE CIRCLE AND THE SPHERE

CHAPTER XII CONIC SECTIONS

CHAPTER XIII QUADRIC SURFACES

CHAPTER XIV AREAS AND VOLUMES

CHAPTER XV INTRODUCTION TO DIFFERENTIAL GEOMETRY

CHAPTER XVI DIFFERENTIAL LINE-GEOMETRY

CHAPTER XVII MULTIPLY CONNECTED SPACES

CHAPTER XVIII THE PROJECTIVE BASIS OF NON-EUCLIDEAN GEOMETRY

CHAPTER XIX THE DIFFERENTIAL BASIS FOR EUCLIDEAN AND NON-EUCLIDEAN GEOMETRY