That a parallel projection of a parallelepiped is a parallelepiped.
The same may be said for the proposition about the diagonal plane of a parallelepiped.
The volume of any parallelepiped is equal to the product of its base by its altitude.
Archimedes proves that the volume of the solid so cut off is one sixth part of the volume of the parallelepiped.
"parallelepiped" is from the Greek parallelos (parallel) and epipedon (a plane surface), from epi (on) and pedon (ground).
The opposite lateral faces of a parallelepiped are congruent and parallel.
Euclid calls this solid henceforth a parallelepiped, though he never defines the word.
The volume of any parallelepiped, or of any triangular prism, is measured by the product of base and altitude.
But a triangular prism is equal in volume to a parallelepiped which has the same base and altitude.