Euclid's Book 10 - Proposition 41

Proposition : If two straight lines incommensurable in square which make the sum of the squares on them medial and the rectangle contained by them medial and also incommensurable with the sum of the squares on them are added together, then the whole straight line is irrational; let it be called the side of the sum of two medial areas.
Lemma : If a straight line AB is cut into unequal parts at each of the points C and D, and AC is greater than DB then the sum of the squares on AC and CB is greater than the sum of the squares on AD and DB.