A Course of Pure Geometry: Containing a Complete Geometrical, Treatment of the Properties of the Conic Sections (Classic Reprint)

Course of Pure Geometry published in 1903. It differs from the former edition in that it does not assume any previous knowledge of the Conic Sections, which are here treated ah initio, on the basis of the definition of them as the curves of projection of a circle. This is not the starting point of the subject generally in works on Geometrical Conic Sections. The curves are usually defined by means of their focus and directrix property, and their other properties are evolved therefrom. Here the focus and directrix propert} is established as one belonging to the projections of a circle and it is freely used, but the fact that the conies are derived by projection from a circle and therefore possess all its projective properties is kept constantl} in the mind of the student. Many of the properties of the Conic Sections which can only be established with great labour from their focus and directrix property are proved quite simply when the curves are derived directly from the circle. Nor is the method employed here any more difficult than the prevalent one, though it is true that certain ground has to be covered first. But this is not very extensive and I have indicated (p. xii) the few articles which aS tudent should master before he proceeds to Chapter
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