Now, we have two questions instead of one. But two questions may be easier to answer than just one question provides that the two questions are intelligently connected.
Laying aside, for the moment, our original problem concerning the tetrahedron, we concentrate upon the simpler analogous problem concerning the triangle. To solve this problem, we have to know something about centers of gravity. The following principle is plausible and presents itself naturally. If a system of masses S consists of parts, each of which has its centre of gravity in the same plane, then this plane contains also the centre of gravity of the whole system S.