◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-11-elementary-stereometry / Proposition: Prop. 11.34: Parallelepipeds are of Equal Volume iff Bases are in Reciprocal Proportion to Heights

Proposition: Prop. 11.34: Parallelepipeds are of Equal Volume iff Bases are in Reciprocal Proportion to Heights

(Proposition 4 from Book 1 of Euclid's “Elements”)¹

The bases of equal parallelepiped solids are reciprocally proportional to their heights. And those parallelepiped solids whose bases are reciprocally proportional to their heights are equal.

• Let $AB$ and $CD$ be equal parallelepiped solids.
• I say that the bases of the parallelepiped solids $AB$ and $CD$ are reciprocally proportional to their heights, and (so) as base $EH$ is to base $NQ$, so the height of solid $CD$ (is) to the height of solid $AB$.

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:

@Fitzpatrick

References

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", https://proofwiki.org/wiki/Main_Page, 2016

Footnotes