Hyperbolic system

Abstract

If we take into consideration only a plane on one side, and a homological hyperboloid on the other, then even in this case we can recognize the relatedness of these linear seconds of points, because the infinitely distant points of the first system, and therefore their complete linear example, are homologous to the points of the straight line of intersection of the hyperboloid with the plane of involution, and consequently this entire straight line as a linear element of extraelements. From here, in particular, it follows that if three arbitrary points are given in the second system, then the spheroprim defined by them can easily be obtained in this way: we project these three points through the center Z onto the plane, construct a circle based on them, and transfer the points of the latter to a parabolic hyperboloid by inverse projection . The center of this spheroprim is also designed. It is clear that this center on the hyperboloid in relation to the spheroprim is the pole of the mentioned straight line on the hyperboloid.