This paper included an analytical proof of the following theorem:

If five spheres 1, 2, 3, 4, 5, pass through the same point, and if the four points in which the four spheres 1, 2, 3, 4, intersect in sets of three be coplanar; and if the same be true for the sets 1, 2, 3, 5; 1, 2, 4, 5; 1, 3, 4, 5; it will also be true for the remaining set 2, 3, 4, 5.

The same theorem is true for similar and similarly situated quadric surfaces.