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Proof: By Euclid

(related to Corollary: 5.19: Proportional Magnitudes have Proportional Remainders)

So (it is) clear, from this, that if composed magnitudes are proportional then they will also be proportional (when) converted.
(Which is) the very thing it was required to show.
∎

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References

Bibliography

Health L. Thomas (Transl.): "Euclid's Elements - all thirteen books", Green Lion Press, 2013,
Byrne, O.: "The First Six Books of the Elements of Euclid, in Which Coloured Diagrams and Symbols are used Instead of Letters", London William Pickering, 1847