Systems of segments and pairs of rays on a plane

Abstract

“In my previous works, I examined a number of geometric systems, the elements of which consist of pairs of points. The simplest and most important of them is the system of parallel vectors, then the system of harmonic segments and vectors, and finally the system of midpoints of harmonic pairs. But in all these systems considered, some limitation is introduced either in the form of vectorality or in the form of a special parameter of the system. Here I mean to consider a system of such elements, given without any restrictions, that is, I imagine that an element of a system on a plane can be an arbitrary pair of its points, which at the same time will form a segment.