Proposition: Prop. 11.30: Parallelepipeds on Same Base and Same Height whose Extremities are not on Same Lines are Equal in Volume

(Proposition 30 from Book 11 of Euclid's “Elements”)

Parallelepiped solids which are on the same base, and (have) the same height, and in which the (ends of the straight lines) standing up are not on the same straight lines, are equal to one another.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2

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Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki",, 2016