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.
