The Ten Books on Architecture, 3.3.12

Vitruvius  translated by Joseph Gwilt

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12The diminution of columns taken at the hypotrachelium, is to be so ordered, that for columns of fifteen feet and under, it should be one-sixth of the lower diameter. From fifteen to twenty feet in height, the lower diameter is to be divided into six parts and a half; and five parts and a half are to be assigned for the upper thickness of the column. When columns are from twenty to thirty feet high, the lower diameter of the shaft must be divided into seven parts, six of which are given to the upper diameter. From thirty to forty feet high, the lower diameter is divided into seven parts and a half, and six and a half given to the top. From forty to fifty feet, the lower diameter of the shaft is to be divided into eight parts, seven of which must be given to the thickness under the hypotrachelium. If the proportion for greater heights be required, the thickness at top must be found after the preceding method;

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