Euclidean Geometry

Authors: Specht, E.J., Jones, H.T., Calkins, K.G., Rhoads, D.H.
Provides a complete and rigorous axiomatic treatment of Euclidean geometry
Proofs for many theorems are worked out in detail
Takes a modern approach by replacing congruence axioms with a transformational definition of congruence

Galilean geometry is the study of the x-t plane under the motions that correspond to changes in time origin and change of uniform motion coordinate system. Although we introduce this geometry on physical grounds, we quickly move on to study this geometry in its own right without any physical motivation.

There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec­ tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising.

This is a reissue of Professor Coxeter's classic text on non-Euclidean geometry. It begins with a historical introductory chapter, and then devotes three chapters to surveying real projective geometry, and three to elliptic geometry.