Two right lines comprised between two parallel planes are always divided into proportional parts by a third plane parallel to the first two.
Trihedral angle.—The sum of any two of the plane angles which compose a trihedral angle is always greater than the third.
The sum of the plane angles which form a convex polyhedral angle is always less than four right angles.
If two trihedral angles are formed by the same plane angles, the dihedral angles comprised between the equal plane angles are equal.—There may be absolute equality or simple symmetry between the two trihedral angles.
Of polyhedrons.
If two tetrahedrons have each a trihedral angle composed of equal and similarly arranged triangles, these tetrahedrons are equal. They are also equal if two faces of the one are equal to two faces of the other, are arranged in the same manner, and form with each other the same dihedral angle.
When the triangles which form two homologous trihedral angles of two tetrahedrons are similar, each to each, and similarly disposed, these tetrahedrons are similar. They are also similar if two faces of the one, making with each other the same angle as two faces of the other, are also similar to these latter, and are united by homologous sides and summits.
Similar pyramids.—A plane parallel to the base of a pyramid cuts off from it a pyramid similar to it.—To find the height of a pyramid when we know the dimension of its trunk with parallel bases.
Sections made in any two pyramids at the same distance from these summits are in a constant ratio.
Parallelopipedon.—Its diagonals.