About special circles and spheres

Abstract

In my article on the system of spheres, I outlined their linear and spherical aggregates, the collinear and reciprocal transformation of these aggregates, but did not touch at all the special circles found in each of their linear patterns. It was only implied that among all the circles of such a prima there is a circle of infinitely large radius , and such a circle is a straight line constituting the radical axis of the prima. As if in contrast to this, in the scientific literature, starting with Shteiner, it is understood that in the linear example of circles the special one is not a straight line, but a pair of straight lines, one of which is the radical axis, and the other is the infinitely distant straight line; but I am not aware that the question of special circles has been specifically discussed anywhere. With this note I intend to fill this gap.