Proposition: 7.17: Multiples of Ratios of Numbers
(Proposition 17 from Book 7 of Euclid's “Elements”)
If a number multiplying two numbers makes some (numbers) then the (numbers) generated from them will have the same ratio as the multiplied (numbers).
 For let the number $A$ make (the numbers) $D$ and $E$ (by) multiplying the two numbers $B$ and $C$ (respectively).
 I say that as $B$ is to $C$, so $D$ (is) to $E$.
Modern Formulation
In modern notation, this proposition states that if \[d = a\,b\quad\text{ and }\quad e=a\,c,\] then \[\frac de=\frac bc,\] where all symbols denote numbers.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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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