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Proposition: Prop. 11.17: Straight Lines cut in Same Ratio by Parallel Planes

(Proposition 17 from Book 11 of Euclid's “Elements”)

If two straight lines are cut by parallel planes then they will be cut in the same ratios.

• For let the two straight lines $AB$ and $CD$ be cut by the parallel planes $GH$, $KL$, and $MN$ at the points $A$, $E$, $B$, and $C$, $F$, $D$ (respectively).
• I say that as the straight line $AE$ is to $EB$, so $CF$ (is) to $FD$.

Modern Formulation

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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