If two numbers multiplying some number make some (other numbers) then the (numbers) generated from them will have the same ratio as the multiplying (numbers). * For let the two numbers $A$ and $B$ make (the numbers) $D$ and $E$ (respectively, by) multiplying some number $C$. * I say that as $A$ is to $B$, so $D$ (is) to $E$.
In modern notation, this propositions states that if \[a\,c = d\quad\text{ and }\quad b\,c=e,\] then \[\frac ab=\frac de,\] where all symbols denote numbers.
Proofs: 1