The minutes of a decade of argument between the Milanese building council and a series of foreign experts over how high, how wide and how strong the new cathedral should be: the only surviving record of Gothic masons debating the principles of their art aloud.
Milan Cathedral was begun in 1386 on a scale that the local builders, trained in brick, had never attempted in stone. Its five-aisled plan was already fixed at a total width of 96 braccia (a Milanese braccio is roughly 0.6 m). What was not fixed was the section: how high the nave and aisles should rise, and by what rule. To settle this the council, the Fabbrica, summoned experts from beyond the Alps and recorded their meetings in its annals.
In 1391 the German master Hans von Freiburg was followed by the mathematician Gabriele Stornaloco of Piacenza, who was asked to calculate a section ad triangulum, fitted to an equilateral triangle standing on the width. The height of such a triangle is irrational, and Stornaloco proposed rounding it to 84 braccia so that it could be divided into six equal units of 14. In 1392 Heinrich Parler of Gmünd argued for ad quadratum: a section as high as it was wide, 96 braccia. The council put a list of questions to the vote and chose the lower course, reducing the upper levels further still.
The sharpest exchanges came in 1399–1401 with Jean Mignot, a master from Paris, who listed dozens of faults in the work and warned that the piers and buttresses were too weak. When the Milanese answered that pointed arches do not push on their buttresses, and that geometry had no business overruling experience, Mignot replied with the phrase that has become the motto of the whole affair: ars sine scientia nihil est, “art without science is nothing”. By scientia he meant the geometrical rules of the lodges; by ars, the practical skill of building. The Milanese countered that science without art was nothing either.
The building did not fall down. But the debates are precious because they show that Gothic design was guided by explicit geometrical procedures (squares, triangles, modules) that masters could name, defend and argue over, and that those procedures were understood, even then, as a way of making a building both beautiful and sound.
The book, part by part
I 1391: Stornaloco and the triangle
The section fitted to an equilateral triangle on the 96-braccia width, its height rounded to 84 braccia, six units of 14.
II 1392: Parler and the square
Heinrich Parler’s case for a section as high as it is wide; the council’s vote for a lower solution.
III 1399–1401: Mignot on art and science
Jean Mignot’s critique of the piers, buttresses and the claim that pointed arches do not thrust; the exchange over ars and scientia.