Collinear transformation of imaginary pairs of rays

Abstract

Involutory-collinear transformations belong to the most elementary operations of the new geometry. However, this always refers to the transformation of real geometric figures. The problem of transforming imaginary figures, e.g., imaginary circles, appears not to have been posed and seems incomprehensible. In the study of a system of pairs of rays, this problem presented itself in all its reality in the following form. If two pairs of rays are given, we take them as two pairs of tangents to a parabola, which we easily construct, and thus we find the linear prima of pairs of rays, the centers of which constitute a line, and the pairs of rays themselves are pairs of tangents to the parabola.

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