(related to Proposition: 7.26: Product of Co-prime Pairs is Co-prime)

- For since $A$ and $B$ are each prime to $C$, the (number) created from (multiplying) $A$ and $B$ will thus also be prime to $C$ [Prop. 7.24].
- And $E$ is the (number) created from (multiplying) $A$ and $B$.
- Thus, $E$ and $C$ are prime to one another.
- So, for the same (reasons), $E$ and $D$ are also prime to one another.
- Thus, $C$ and $D$ are each prime to $E$.
- Thus, the (number) created from (multiplying) $C$ and $D$ will also be prime to $E$ [Prop. 7.24].
- And $F$ is the (number) created from (multiplying) $C$ and $D$.
- Thus, $E$ and $F$ are prime to one another.
- (Which is) the very thing it was required to show.∎

**Fitzpatrick, Richard**: Euclid's "Elements of Geometry"