For, since the sum of the squares on AB, BC is rational, while twice the rectangle AB, BC is medial,
therefore the squares on AB, BC are incommensurable with twice the rectangle AB, BC;
and, convertendo, the squares on AB, BC are incommensurable with the remainder, the square on AC. [II. 7, X. 16]
But the squares on AB, BC are rational;
therefore the square on AC is irrational;
therefore AC is irrational.
And let it be called minor.