A short printed booklet by the master of works of Regensburg Cathedral showing, step by step, how to draw the plan and elevation of a pinnacle from a single square, the first printed book devoted to a problem of Gothic design, and a window into the geometry that lodges had long kept among themselves.
Mathes Roriczer came from a family of masons who ran the works at Regensburg Cathedral for three generations. In 1486 he printed his booklet on the “correct” (gerecht) design of a pinnacle, dedicated to the bishop of Eichstätt, and soon after a companion on gablets (the Wimpergbüchlein) and a small practical geometry. That a lodge master should put such rules into print, where anyone could buy them, was itself a sign that the closed world of the Gothic lodges was changing.
The method uses nothing but compasses and a straight-edge. Draw a square the width of the pinnacle. Join the mid-points of its sides to make a second square, turned through 45°, half the area of the first; join the mid-points of that to make a third, and so on. Turn the second and third squares back square to the first, and the nested set gives, in plan, the body of the pinnacle, the recesses of its panels and the base of its spire. The elevation is then raised from the plan: every height is taken as a multiple of the side of the first square.
Nothing is measured and no arithmetic is needed: every dimension follows from the first by construction, which is exactly what made such procedures portable from lodge to lodge. Roriczer’s pinnacle is a small object, but the principle (derive the part from the whole by a chain of geometrical steps) is the principle of ad quadratum design at every scale, from pinnacles to the sections of cathedrals.
The book, part by part
I The plan
A square; a second on the mid-points of the first; a third on the mid-points of the second. Rotated back into line, the nested squares give the widths of body, panels and spire.
Rules: A pinnacle from one square
II The elevation
The heights of the body (Leib) and spire (Riese), the gablets on each face and the finial, all taken as multiples of the base square’s side, so that the whole pinnacle scales with a single choice.
Rules: The pinnacle is a weight