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Published online by Cambridge University Press: 03 November 2016
While the conception of the Circle at Infinity as a weapon for analytical investigation has been fairly often applied (as for example “Some equations connected with the Plane Section of the Conicoid” by the author, Math. Gaz., July 1933), its use as the basis for descriptive enquiry has been rarer and disconnected. The aim of this paper is to obtain by simple steps the principal descriptive properties of the quadric surfaces from their intersections with the Plane and Circle at Infinity. The method also has the advantage of making manifest how the basic causes of the differences between the properties of different types of quadric arise, which are often hidden in algebraic treatment.
Page 195 of note * The assumptions which have been made with respect to the quadric are, the existence of a tangent plane, the tangent cone, its plane of contact as the polar plane and the polar line.