The Elements of Non-Euclidean Geometry (Classic Reprint)

The present work is an extension and elaboration of a course of lectures on Non-E uclidean Geometry which I dehvered at the Colloquium held under the auspices of theE dinburgh Mathematical Society in A ugust, 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 euchdean geometry as a really degenerate form in the sense in which a pair of straight hues 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-eucH dean geometry can fully elucidate.
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