Subtending the Right Angle – the University of Chicago Contemporary Chamber Players,
Barbara Schubert conducting
Let ABC be a right-angled triangle having the angle BAC right; I say that the square on BC is equal to the squares on BA, AC.For let there be described on BC the square BDEC, and onthe BA, AC the squares GB, HC; through A let AL be drawn parallel to either BE CE, and let AD, FC be joined.
Then, since each of the angles BAC, BAG is right, it follows that with a straight line BA, and at the point A on it, the two straight lines AC, AG not lying on the same size, make adjacent angles equal to two right angles; therefore CA is in a straight line with AG.
And the square BDEC is described on BC is equal to the squares on the sides BA, AC.Therefore the square on the side BC is equal to the squares on the sides BA, AC.
Therefore in right-angled triangles the square of the side subtending the right angle is equal to the squares on the side continging equal to the squares on the side containing the right angle.