◀ ▲ ▶Branches / Geometry / Elementseuclid / Book11elementarystereometry / Proposition: Prop. 11.37: Four Straight Lines are Proportional iff Similar Parallelepipeds formed on them are Proportional
Proposition: Prop. 11.37: Four Straight Lines are Proportional iff Similar Parallelepipeds formed on them are Proportional
Euclid's Formulation
If four straight lines are proportional then the similar, and similarly described, parallelepiped solids on them will also be proportional. And if the similar, and similarly described, parallelepiped solids on them are proportional then the straight lines themselves will be proportional.
 Let $AB$, $CD$, $EF$, and $GH$, be four proportional straight lines, (such that) as $AB$ (is) to $CD$, so $EF$ (is) to $GH$.
 And let the similar, and similarly laid out, parallelepiped solids $KA$, $LC$, $ME$ and $NG$ have been described on $AB$, $CD$, $EF$, and $GH$ (respectively).
 I say that as $KA$ is to $LC$, so $ME$ (is) to $NG$.
Modern Formulation
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Table of Contents
Proofs: 1
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016
Footnotes