Page 72
XXIX.
THere are divers wayes to lessen Collumns, whereof I have here and in the following page set down those two which are most esteemed of. The first and best is this▪ After you know the height and thickness of the Column, you must divide the Cathetus thereo•• into 3 equal parts, and in the point of the first division upwards, draw a thwart line through the Column, that shall cut the Cathetus at right Angles, then in the point of Intersection, set one foot of your Compasses, and extend the other foot to one of the sides of the Column, or to half the bredth, which is all one, and so describe a Semi-circle upon the thwart line, then divide half that Semicircle into so many parts as you please, as into 6, 9, 12, 15, or more, and no••e that into so many parts as you divide the Semi-circle, so many equall parts you must divide the two upper thirds of the Cathetus into, and upon every Division draw straight Lines through the Column, that shall cut the Cathetus at right Angles; then from every point of Division in the Semicircle, draw straight Lines parallel to the Cathetus, and where these straight lin••s intersect the Lines drawn athwart the Column, there shall be the severall points that you must lessen the Column into in every particular place. But you must take notice, that the Line drawn from the first point of Division in the Sem••circle, must intersect the line drawn from the first Division in the Cathetus; and the second in the Semicircle, the line drawn from the second in the Cathe∣tus; the third in the Semi-circle, from the third in the Cathetus, and so forth; every line drawn from the severall points of Division in the Semi-circle, must intersect the line drawn from the same number of Divisions in the Cathetus.
Having thus drawn one side of the Column, you may by the same Rules draw the other side also, or else measuring with your Compasses the distance of every point of lessening from the Cathetus, you need but turn your Com∣p••sses about upon the point that stands in the Cathetus, and so transfer the distance to the other side of the Column.
This kind of lessening may be used in the Tuscan and Dorick Order, which Orders are not to be lessened below the nethermost third part of the Column.