Any polyhedron can always be divided into triangular pyramids.—Two bodies composed of the same number of equal and similarly disposed triangular pyramids, are equal.
Similar polyhedrons.
The homologous edges of similar polyhedrons are proportional; as are also the diagonals of the homologous faces and the interior diagonals of the polyhedrons.—The areas of similar polyhedrons are as the squares of the homologous edges.
Measure of volumes.
Two parallelopipedons of the same base and of the same height are equivalent in volume.
If a parallelogram be constructed on the base of a triangular prism, and on that parallelogram, taken as a base, there be constructed a parallelopipedon of the same height as the triangular prism, the volume of this prism will be half of the volume of the parallelopipedon.—Two triangular prisms of the same base and the same height are equivalent.
Two tetrahedrons of the same base and the same height are equivalent.
A tetrahedron is equivalent to the third of the triangular prism of the same base and the same height.
The volume of any parallelopipedon is equal to the product of its base by its height.—What must be understood by that enunciation.—The volume of any prism is equal to the product of its base by its height.
The volume of a tetrahedron and that of any pyramid are measured by the third of the product of the base by the height.