The Ten Books on Architecture, 4.3.9

Vitruvius  translated by Morris Hicky Morgan

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9The columns should be fluted with twenty flutes. If these are to be left plane, only the twenty angles need be marked off. But if they are to be channelled out, the contour of the channelling may be determined thus: draw a square with sides equal in length to the breadth of the fluting, and centre a pair of compasses in the middle of this square. Then describe a circle with a circumference touching the angles of the square, and let the channellings have the contour of the segment formed by the circumference and the side of the square. The fluting of the Doric column will thus be finished in the style appropriate to it.

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