Vorlesungen über Nicht-Euklidische Geometrie (Grundlehren der mathematischen Wissenschaften) (German Edition)

This classic in geometry represents Klein's approach to non-Euclidean geometry, including his contribution to the fundamental question of the consistency of non-Euclidean geometry. The first part of the book is an overview of projective geometry. The second part contains Klein's remarkable work on embedding both Euclidean and non-Euclidean geometry into the framework of projective geometry. The most significant consequence of this was the equivalence of the consistency of Euclidean geometry with the consistency of non-Euclidean (Lobachevskian) geometry in the plane. There is, of course, much more in this volume, as Klein applies his surprisingly modern point of view to the fundamental problems of geometry of his era. The text is in German.