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 $E$.
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.
Proofs: 1
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