Non-Euclidean geometry

摘要: Throughout most of this book, non-Euclidean geometries in spaces two or three dimensions are treated as specializations real projective geometry terms a simple set axioms concerning points, lines, planes, incidence, order and continuity, with no mention the measurement distances angles. This synthetic development is followed by introduction homogeneous coordinates, beginning Von Staudt's idea regarding points entities that can be added multiplied. Tranformations preserve incidence called collineations. They lead natural way to isometries 'congruent transformations'. Following recommendation Bertrand Russell, continuity described order. Elliptic hyperbolic derived from specializing an elliptic polarity which transforms into lines (in dimensions) planes vice versa.