◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-11-elementary-stereometry / Proposition: Prop. 11.36: Parallelepiped formed from Three Proportional Lines equal to Equilateral Parallelepiped with Equal Angles to it forme

Proposition: Prop. 11.36: Parallelepiped formed from Three Proportional Lines equal to Equilateral Parallelepiped with Equal Angles to it forme

(Proposition 36 from Book 11 of Euclid's “Elements”)

If three straight lines are in (continued) proportion then the parallelepipedal solid (formed) from the three (straight lines) is equal to the equilateral parallelepipedal solid on the middle (straight line which is) equiangular to the aforementioned (parallelepipedal solid).

• Let $A$, $B$, and $C$ be three straight lines in (continued) proportion, (such that) as $A$ (is) to $B$, so $B$ (is) to $C$.
• I say that the (parallelepiped) solid (formed) from $A$, $B$, and $C$ is equal to the equilateral solid on $B$ (which is) equiangular with the aforementioned (solid).

Modern Formulation

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Table of Contents

Proofs: 1

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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