Proof: By Euclid
(related to Proposition: 7.12: Ratios of Numbers is Distributive over Addition)
 For since as $A$ is to $B$, so $C$ (is) to $D$, thus which(ever) part, or parts, $A$ is of $B$, $C$ is also the same part, or parts, of $D$ [Def. 7.20] .
 Thus, the sum $A$, $C$ is also the same part, or the same parts, of the sum $B$, $D$ that $A$ (is) of $B$ [Prop. 7.5], [Prop. 7.6].
 Thus, as $A$ is to $B$, so $A$, $C$ (is) to $B$, $D$ [Def. 7.20] .
 (Which is) the very thing it was required to show.
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"