Proposition: Prop. 11.32: Parallelepipeds of Same Height have Volume Proportional to Bases

(Proposition 32 from Book 11 of Euclid's “Elements”)

Parallelepiped solids which (have) the same height are to one another as their bases. * Let $AB$ and $CD$ be parallelepiped solids (having) the same height. * I say that the parallelepiped solids $AB$ and $CD$ are to one another as their bases.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2 3 4

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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