The Ten Books on Architecture, 6.3.4

Vitruvius  translated by Joseph Gwilt

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4Their height, to the underside of the beams, is to be one-fourth less than the length; the remaining fourth is assigned for the proportion of the lacunaria and roof above the beams. The width of the alæ, on the right and left, when the atrium is from thirty to forty feet long, is to be one third part thereof. From forty to fifty feet, the length must be divided into three parts and a half; of these, one is given to the alæ: but when the length is from fifty to sixty feet, a fourth part thereof is given to the alæ. From sixty to eighty feet, the length is divided into four parts and a half, of which one part is the width of the alæ. From eighty feet to one hundred, the length is divided into five parts, and one of them is the true width of the alæ. The lintel beams (trabes liminares) are placed at a height which will make the breadths and heights equal.

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