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I.47 Proposition I.47
In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.
Proof
Erect squares on each side via I.46; using I.14, I.31 and I.41 show
each part-square equals a corresponding parallelogram cut off the
hypotenuse-square by the perpendicular from the right angle; sum via
Common Notion 2.
Figure
