The proof usually given of Von Staudt's Theorem is entirely analytical in character. The following proof is geometrical:—

If A, B, C, D be the vertices of a tetrahedron whose opposite faces are α., β, γ, δ, and if l be any line, to prove that l [ABCD] = l [αβγδ] where lA denotes the plane through the line l and the point A and lα. denotes the intersection of the line l with the plane α.