Euclid's Book 10 - Proposition 33

Lemma : Let ABC be a right-angled triangle having the angle A right, and let the perpendicular AD be drawn. Then the rectangle CB by BD equals the square on BA, the rectangle BC by CD equals the square on CA, the rectangle BD by DC equals the square on AD, and the rectangle BC by AD equals the rectangle BA by AC, and first that the rectangle CB by BD equals the square on BA.
Proposition : To find two straight lines incommensurable in square which make the sum of the squares on them rational but the rectangle contained by them medial.
• Book on Geometry - Dow...