The Ten Books on Architecture, 5.11.3

Vitruvius  translated by Morris Hicky Morgan

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3But on the outside, let three colonnades be arranged, one as you leave the peristyle and two at the right and left, with running-tracks in them. That one of them which faces the north should be a double colonnade of very ample breadth, while the other should be single, and so constructed that on the sides next the walls and the side along the columns it may have edges, serving as paths, of not less than ten feet, with the space between them sunken, so that steps are necessary in going down from the edges a foot and a half to the plane, which plane should be not less than twelve feet wide. Thus people walking round on the edges will not be interfered with by the anointed who are exercising.

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