Here's Proposition 2 from Book 5 of Euclid's _Elements_ :
> If a first magnitude and a third are equal multiples of a second and a fourth, and a fifth and a sixth are equal multiples of the second and fourth, then the first magnitude and fifth, being added together, and the third and the sixth, being added together, will also be equal multiples of the second and the fourth, respectively.
Or in modern notation: $a(x + y) = ax + ay$.