PARALLELOPIPED

, or Parallelopipedon, is a solid figure contained under six parallelograms, the opposites of which are equal and parallel. Or, it is a prism whose base is a parallelogram.

Properties of the Parallelopipedon.—All Parallelopipedons, whether right or oblique, that have their bases and altitudes equal, are equal; and each equal to triple a pyramid of an equal base and altitude.—A diagonal plane divides the Parallelopipedon into two equal triangular prisms.—See other properties under the general term Prism, of which this is only a particular species.

To Measure the Surface and Solidity of a PARALLELOPIPEDON.—Find the areas of the three parallelograms AD, BE, and BG, which add into one sum; and double that sum will be the whole surface of the Parallelopipedon.

For the Solidity; multiply the base by the altitude; that is, any one face or side by its distance from the opposite side; as AD × DE, or AB × BE, or BG × BD.