Steven J. Foundations of Geometry 2022

Textbook in PDF format

Our study of geometry begins with an examination of the historical origins of the axiomatic method in geometry. While the material in this chapter is not a mathematical prerequisite for what comes later, an appreciation of the historical roots of axiomatic thinking is essential to an understanding of why the foundations of geometry are systematized as they are.
Prologue: Euclidв’s Elements
Axiomatic Systems and Incidence Geometry
Axioms for Plane Geometry
Neutral Geometry
Euclidean Geometry
Hyperbolic Geometry
Area
Circles
Constructions
Transformations
Models
Polygonal Models and the Geometry of Space
Appendices
A Euclidв’s Book
B Systems of Axioms for Geometry
C The Postulates Used in this Book
D The van Hiele Model