Systems of circles on a sphere

Abstract

Any general collection of circles will not differ from the collection of circles of the previous system, but will constitute only half of the collection of this system, and the linear primes and seconds of ordinary circles will remain the same for this system; but the linear collections of vector circles of the previous system will no longer be such for this system , because the tangent linear primes of the previous one are no longer the linear primes of this system. It is easy to prove that in this system there are no collections of vector circles at all; they cannot even be specified. In fact, if I think about, for example, a right vectorial circle, then diametrically opposite to it is already a left vectorial circle; in essence, two vectorial circles are obtained, which completely and unambiguously determine their linear primacy on the sphere; it is clear that in her presence it is impossible to set a third, arbitrary circle; in general, it would no longer be part of a certain linear prima.