Ad quadratum and ad triangulum
A cathedral section proportioned from the square or the equilateral triangle, as argued at Milan in 1391–1401.
The rules it illustrates
Halve a square by turning a square within it. To make a square of half the area of another, join the mid-points of its sides: the rotated square so drawn has exactly half the area. Repeat to halve again.
Ad quadratum: a section as high as it is wide. Proportion the cross-section of a church from the square: let the total height to the crown of the nave vault equal the total width, and take the heights of the aisles and the springing of the vaults at whole divisions of that square.
Ad triangulum: the equilateral triangle. Alternatively, fit the section to an equilateral triangle standing on the width, so that the height is √3⁄2 of the width, and take the levels at equal divisions of that height.
Where it appears in the book
In the chapters Romanesque and Gothic.