If two straight lines incommensurable in square which make the sum of the squares on them medial, but the rectangle contained by them rational, be added together, the whole straight line is irrational; and let it be called theside of a rational plus a medial area.

For let two straight lines AB, BC incommensurable in square, and fulfilling the given conditions [X. 34
], be added together; I say that AC is irrational.