Quadratic thirds and seconds of rays

Abstract

The thirds of rays, representing the so-called zero systems and completely and uniquely determined by five arbitrary rays, are usually called linear in view of the fact that in each plane and from each point in space there is a prima of rays intersecting at one point and contained in one plane; such a prima of rays in a plane or emanating from one center is called linear. But for a system of rays, defined as a parameter by a special extra-ray, such primes are no longer linear, since the latter must necessarily contain this extra-ray. Therefore, the zero systems themselves do not represent linear thirds in this system, but these are quadratic thirds.