Construction of a curved surface of the 2nd order (conoseconds) from imaginary pairs of points or an imaginary conic section.

Abstract

We know that from two given points e with e' and a conical section K on the plane, we can reproduce a curved surface of the 2nd order, if from these points we take one e as the center of the second of the rays, and the second e' as the center of the second of the planes and bring these two seconds into a correlative relation so that the ray ea (a point on the conic section plane) will be considered correlative to the plane e'A, where A is the polar of the 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.