7. The surface of a sphere is two thirds of the whole surface of its circumscribed cylinder.
8. If the four diagonals of a quadrangular prism be concurrent, it is a parallelopiped.
9. If the slant height of a right cone be equal to the diameter of its base, its total surface is to the surface of the inscribed sphere as 9 : 4.
10. The middle points of two pairs of opposite edges of a triangular pyramid are coplanar, and form a parallelogram.
11. If the four perpendiculars from the vertices on the opposite faces of a pyramid ABCD be concurrent, then
12. Every section of a sphere by a plane is a circle.
13. The locus of the centres of parallel sections is a diameter of the sphere.
14. If any number of lines in space pass through a fixed point, the feet of the perpendiculars on them from another fixed point are homospheric.
15. Extend the property of Ex. 4 to the pyramid.