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7so that the number of feet contained in the two areas of the square of three and four feet added together, are equal to those contained in the square, whose side is five feet. When Pythagoras discovered this property, convinced that the Muses had assisted him in the discovery, he evinced his gratitude to them by sacrifice. This proposition is serviceable on many occasions, particularly in measuring, no less than in setting out the staircases of buildings, so that each step may have its proper height.
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