Proposition: 7.11: Proportional Numbers have Proportional Differences
(Proposition 11 from Book 7 of Euclid's “Elements”)
If as the whole (of a number) is to the whole (of another), so a (part) taken away (is) to a (part) taken away, then the remainder will also be to the remainder as the whole (is) to the whole.
 Let the whole $AB$ be to the whole $CD$ as the (part) taken away $AE$ (is) to the (part) taken away $CF$.
 I say that the remainder $EB$ is to the remainder $FD$ as the whole $AB$ (is) to the whole $CD$.
Modern Formulation
In modern notation, this proposition states that if \[\frac{AB}{CD}=\frac{AE+EB}{CF+FD}=\frac{AE}{CF},\] then \[\frac{EB}{FD}=\frac{AB}{CD}.\]
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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