About systems whose linear prims are determined by three elements

Abstract

If it is impossible to unambiguously determine an infinite set of rays from arbitrarily given two of them, then this can be achieved from arbitrarily given three of them. It is well known from elementary manuals that with three arbitrary given lines, and, moreover, non-intersecting lines, one can completely and unambiguously determine a certain unisexual hyperboloid. Since this curved surface of the 2nd order consists not of one, but of two systems of non-intersecting straight lines, it is clear that from the three straight lines only one of them is directly determined, which includes three data, and then it is logically inevitable to also accept the other a collection that occupies a position in space identical to the first system, that is, the surface of a unisexual hyperboloid.