Column heights in modules

An arch pushes outward on its supports as well as down. For the same load and span the horizontal push grows as the rise falls: halve the rise and you roughly double the thrust.

H ≈ w·s² ⁄ 8f (uniform load w per metre, span s, rise f)

To find how thick the pier of an arch must be, divide the intrados into three equal parts; draw a line from the springing through the first division, and produce it beyond the springing by its own length. A vertical through the end of that line marks the outer face of the pier.

pier ≈ ¼ span (semicircle) · ≈ 0.23 span (equilateral) · less for a lancet

Proportion every step so that twice its height plus its depth equals the length of a natural pace on the level: two feet, or 24 pouces.

2 r + g = 24 pouces ≈ 65 cm (modern practice: 60–66 cm)

Hold that the beauty of the orders comes from fixed proportions that please by nature, as consonances do in music; where the ancients differ, the differences answer to circumstances such as distance and height.

Keep every triglyph centred over a column and every intercolumniation equal, and finish the frieze at the corner with a half-metope half a module wide.

corner semi-metope = ½ M (Vitruvius); equal intercolumniations throughout

Judge every building against the first shelter: four trees for columns, branches laid across them for the entablature, and a pitched roof whose end makes the pediment. These three are the essential parts; all else is added.