Systems of segments and pairs of rays on the plane

Abstract

In my previous works, I examined a number of geometric systems whose elements consist of pairs of points. The simplest and most important of these is the system of parallel vectors, then the systems of harmonic segments and vectors, and finally the system of midpoints of harmonic pairs. However, in all of these systems considered, a certain restriction is introduced, either in the form of vectoriality or in the form of a special parameter of the system. Here I intend to consider a system of such elements given without any restriction; that is, I conceive that an element of the system on the plane can be an arbitrary pair of its points, which simultaneously constitutes a segment.

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