Volumes of Pyramids and Wedges as Equivalent Slabs
A pyramid equals a block of its base by a third of its height; a wedge, by half its height
Three notes give rules for the bulk of solids as equivalent flat blocks. A slab, cube, or cylinder built on the whole base of a pyramid and one third of its height equals that pyramid in quantity; the same block built on the whole base of a wedge (cuneo) and half its height equals the wedge. A third note, keyed to a pyramid lettered a b c d e (base a b c d, apex e), states that a four-sided pyramid must be divided at its base into two triangles and cut through to the apex. The margins show the pyramids, wedges, and prisms-within-cylinders that these rules measure.
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A pyramid equals its base times a third of its height
The slab, cube, or cylinder made from the whole base of a pyramid and a third of its height is equal in quantity to that pyramid. The rule reduces the measure of a pyramid to a flat block of the same volume.
A wedge equals its base times half its height
Likewise the slab, cube, or cylinder made from the whole base of a wedge and half its height is equal to the body of that wedge. The wedge is thus measured against an equivalent rectangular block.
Dividing a four-sided pyramid a b c d e
Every pyramid with unequal sides, being of four sides, must be divided at its base into two triangles, and cut with the same division up to the apex. Thus for pyramid a b c d e, a b c d is the base and e the apex.