Proposition: 8.05: Ratio of Products of Sides of Plane Numbers
(Proposition 5 from Book 8 of Euclid's “Elements”)
Plane numbers have to one another the ratio compounded^{1} out of (the ratios of) their sides.
 Let $A$ and $B$ be plane numbers, and let the numbers $C$, $D$ be the sides of $A$, and (the numbers) $E$, $F$ (the sides) of $B$.
 I say that $A$ has to $B$ the ratio compounded out of (the ratios of) their sides.
Modern Formulation
If $A=CD$ and $B=EF$ then $\frac AB=\frac CE\cdot \frac DF.$
Table of Contents
Proofs: 1
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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
Footnotes