Proof: By Euclid
(related to Proposition: Prop. 9.07: Product of Composite Number with Number is Solid Number)
- For since $A$ is a composite (number), it will be measured by some number.
- Let it be measured by $D$.
- And, as many times as $D$ measures $A$, so many units let there be in $E$.
- Therefore, since $D$ measures $A$ according to the units in $E$, $E$ has thus made $A$ (by) multiplying $D$ [Def. 7.15] .
- And since $A$ has made $C$ (by) multiplying $B$, and $A$ is the (number created) from (multiplying) $D$, $E$, the (number created) from (multiplying) $D$, $E$ has thus made $C$ (by) multiplying $B$.
- Thus, $C$ is solid, and its sides are $D$, $E$, $B$.
- (Which is) the very thing it was required to show.
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"