◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--8-continued-proportion / Proposition: 8.05: Ratio of Products of Sides of Plane Numbers

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 compounded¹ 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)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016

Footnotes