Hyperbolic system

Abstract

If we consider only the plane on one side and the homological hyperboloid on the other, we can still recognize the kinship of these linear secunds of points, because the points at infinity of the first system, and consequently their entire linear prima, are homologous to the points of the line of intersection of the hyperboloid with the plane of involution, and consequently to this entire line as the linear prima of extra-elements. From this, in particular, it follows that if three arbitrary points are given in the second system, the spheroprima determined by them is easily obtained as follows: we project these three points through center Z onto the plane, construct a circle through them, and transfer the points of the latter by inverse projection onto the parabolic hyperboloid. The center of this spheroprima is projected in the same way. It is clear that this center on the hyperboloid, with respect to the spheroprima, is the pole of the aforementioned line on the hyperboloid.

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