5. If two of the plane angles of a tetrahedral angle be equal, the planes of these angles are equally inclined to the plane of the third angle, and conversely. If two of the planes of a trihedral angle be equally inclined to the third plane, the angles contained in those planes are equal.
6. The three lines of intersection of three planes are either parallel or concurrent.
7. If a trihedral angle O be formed by three right angles, and A, B, C be points along the edges, the orthocentre of the triangle ABC is the foot of the normal from O on the plane ABC.
8. If through the vertex O of a trihedral angle O—ABC any line OD be drawn interior to the angle, the sum of the rectilineal angles DOA, DOB, DOC is less than the sum, but greater than half the sum, of the face angles of the trihedral.
9. If on the edges of a trihedral angle O—ABC three equal lines OA, OB, OC be taken, each of these is greater than the radius of the circle described about the triangle ABC.
10. Given the three angles of a trihedral angle, find, by a plane construction, the angles between the containing planes.
11. If any plane P cut the four sides of a Gauche quadrilateral (a quadrilateral whose angular points are not coplanar) ABCD in four points, a, b, c, d, then the product of the four ratios
is plus unity, and conversely, if the product
