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If we draw out from the center of the circle to the base of this triangle a vertical line, then the two angles formed on both sides of this vertical line will be right-angled, and the [original] triangle, due to this drawn out vertical line, will be halved into two right-angled triangles, and the two lines falling on the two extremities [of the locus of contact] will become hypotenuses of these two right-angled triangles, and the vertical line becomes a hypotenuse of [i. The resulting new hypotenuse evidently is larger than the hypotenuse for the right angle. Diaconis speculates that Archimedes might have been using the Stomachion to construct a pictorial proof of some geometric result such as the Pythagorean theorem, the famous equation relating the lengths of the two shorter sides of a right triangle and the length of the hypotenuse. |
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