Villard’s cloister

A leaf of the portfolio of Villard de Honnecourt, worked over about 1250 or 1260 by a later hand that scholars call Magister II, gathers small figures for the building site under the words “Totes ces figures sont estraites de geometrie”: all these figures are taken from geometry. One is a square drawn inside a square, and under it: “Ar chu fait om on clostre, autretant es voies com el prael”, so one makes a cloister, as much in the walks as in the garth. The inner square then holds half of the whole. Here two diameters at right angles are raised in a circle, and swings at its own opening about their four ends cross at the corners of the cloister, whose sides touch the circle at those ends. The diagonals cut the same circle at the corners of the garth, an upright square inside the first. Turned a quarter round, the garth stands on the middles of the four sides, and drawn over it the two make a star of eight points. Folding the four corners of the cloister in covers the turned square exactly: the walks hold as much as the garth, and the figure is exact.