Quadratic ray primes of rays

Abstract

In an article on linear sets of rays, I showed that a system of rays is not an independent system, but that for it it is necessary to take a parameter in the form of an extra ray, which is necessarily part of the linear sets. Then the linear prima is determined completely and unambiguously by two, the linear second by three and the linear third by four arbitrary rays. If three arbitrary rays are given, then together with the constant fourth extra ray we obtain the necessary and sufficient data to determine the rays of a full linear second. Since four arbitrary rays in the general case are intersected by a pair of secants, real or imaginary, it is clear that we can define a linear second only as a set of rays intersecting a given pair of straight lines a and b. For simplicity, we will assume that it is real. Let us denote the extraray defined by the extrapoints of these two common secants by e.