Spherical sets of curves of the 2nd order (conoprim)

Abstract

Let us consider systems of curves of the 2nd order (conoprim). In the system of synonyms of points, circles can be taken as extraelements, because these elements constitute a special system in themselves, and at the same time, any curve with a circle defines a linear prima. In general, in a linear prime there is no such extra element, but only in a linear second. However, you can make a linear second from the linear prima of ordinary (not vector) circles and some other conoprim. Such a linear second, however, will already be special, and therefore should be considered as a special system, and such a system will be related to the system of points on the plane, and the circles of the first must be projective in a special way to the infinitely distant points of the latter. Also, if we compose a linear third from some linear second of circles and some other conoprime, then such a system will be related to the system of points in space. But all these will be special, special systems of connotation points.