Proposition: 5.17: Magnitudes Proportional Compounded are Proportional Separated
(Proposition 17 from Book 5 of Euclid's “Elements”)
If composed magnitudes are proportional then they will also be proportional (when) separated.
 Let $AB$, $BE$, $CD$, and $DF$ be composed magnitudes (which are) proportional, (so that) as $AB$ (is) to $BE$, so $CD$ (is) to $DF$.
 I say that they will also be proportional (when) separated, (so that) as $AE$ (is) to $EB$, so $CF$ (is) to $DF$.
Modern Formulation
In modern notation, this proposition reads that if \[\frac{\alpha+\beta}\beta=\frac{\gamma+\delta}\delta,\] then \[\frac\alpha\beta=\frac\gamma\delta,\]
for all positive real numbers \(\alpha,\beta,\gamma,\delta\).
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4
Sections: 5
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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