Pascal's theorem and its closest analogues on the plane and in space

Abstract

Pascal’s theorem underlies the doctrine of conoprimes, expressing their fundamental property that is completely and unambiguously determined by five elements. It can be expressed in a modern generalized form (see article). This expression clearly demonstrates the deep organic connection of every sixth element with the other five that determine conoprima. A simpler analogue of this theorem can be the well-known theorems expressing the fundamental properties of spheroprimes and spheroseconds.