Construction of a second-order curved surface (a conosecund) from imaginary pairs of points or an imaginary conic section.

Abstract

We know that from two given points eand e' and a conic section K in the plane, we can generate a second‑order curved surface, if we take one of these points, e,as the center of a second of rays, and the other point, e', as the center of a second of planes, and bring these two seconds in a correlative relationship such that to the ray ea (where a is a point on the conic section plane) will be considered correlative to the plane e'A, where A is the polar of point a with respect to the conic section K. It is known that in such a surface a set of rays and their correlative planes intersect.

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