PYRAMID

(Supposed to be from Gr. -xu^, fire, from the resemblance of the form to a spire of flame; but for a more probable derivation pf the word, see infra. Pyramids of Egypt.) In Geometry, a solid contained by a plane; polygonal base and other planes meeting in a point. This point is called the vertex of the pyramid; and the planes which meet in the vertex arc called the sides, which are nece arily all triangles. The principal properties of pyramids are the follow lowing: — 1. Every pyramid is equivalent to one third of a prism having the same base and altitude. Hence, 2. All pyramids having equivalent bases and equal altitudes are equivalent. 3. The solid content of a pyramid is measured by the product of the area of the base into one third of the altitude. 4. If a pyramid is cut by a plane parallel to its base, the frustum (or part comprehended between the base and the section) is equal to the sum of three pyramids having for their common altitude that of the frustum, and of which the bases are respectively the lower base of the frustum, the uf^er base of the frustum, and a mean proportional between them. (See Legendre's Geometry, and Notes.) Pyramids are denominated from the figures of their bases, being triangular, quadrangular, pentagonal, ., according as the base is a triangle, a quadrangle, a pentagon. [s. 1014]