On systems whose linear primes are determined by three elements
Abstract
If it is impossible to uniquely determine an infinite set of rays from two arbitrarily given rays, then this can be achieved based on three arbitrarily given rays. It is well known from elementary textbooks that three arbitrarily given, non-intersecting straight lines, can completely and uniquely determine a certain one-sheeted hyperboloid. Since this curved surface of the second order does not consist of one, but two systems of non-intersecting lines, it is clear that only from one of them, which includes the three given lines, can be determined directly by the three lines, and then it is logically inevitable to also accept the other set which occupies a position in space identical to the first system, i.e., the surface of a hyperboloid of one sheet.
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