NON-EUCLIDEAN BY D. M. Y. SOMMERVILLE, M.A., D.Sc. LECTURER IN MATHEMATICS, UNIVERSITY OF ST. ANDREWS LONDON G. BELL AND SONS, LTD. THE present work is an extension and elaboration of a course of lectures on Non-Euclidean Geometry which I delivered at the Colloquium held under the auspices of the Edinburgh Mathematical Society in August, 1913. Non-euclidean geometry is now a well-recognised branch of mathematics. It is the general type of geometry of homogeneous and continuous space, of which euclidean geometry is a special form. The creation or discovery of such types has destroyed the unique character of euclidean geometry and given it a setting amongst geometrical systems. There has arisen, so to speak, a science of Comparative Geometry. Special care has, therefore, been taken throughout this book to show the bearing of non-euclidean upon euclidean geometry; and by exhibiting euclidean geometry as a really degenerate form-in the sense in which a pair of straight lines is a degenerate conic-to explain the apparent want of symmetry and the occasional failure of the principle of duality, which only a study of non-euclidean geometry can fully elucidate. 301125 |