The Ten Books on Architecture, 9.0.7

Vitruvius  Parallel editions

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Gwilt translation

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.

Morgan translation

7Thus the area in number of feet made up of the two squares on the sides three and four feet in length is equalled by that of the one square described on the side of five. When Pythagoras discovered this fact, he had no doubt that the Muses had guided him in the discovery, and it is said that he very gratefully offered sacrifice to them.

This theorem affords a useful means of measuring many things, and it is particularly serviceable in the building of staircases in buildings, so that the steps may be at the proper levels.