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)
Rules · Cities · Proportion · Façades
The piazza as a double square, framed by porticoes
Make a public square twice as long as it is wide, surround it with porticoes, and keep the buildings round it in proportion to the open space: about a third of its breadth high, and never less than a sixth.
length = 2 × breadth; height of the buildings = ⅓ to ⅙ of the breadth
Alberti takes over Vitruvius’s forum (The forum: two parts broad to three long) and makes it longer, a double square. What matters to him is the relation between the void and its walls: buildings that are too low leave a square looking empty and exposed, buildings that are too high turn it into a well. Continuous porticoes, with arches or with architraves, give the square a uniform frame and give citizens a sheltered place to walk and talk.
In this town the piazza is 176 × 88 m and its arcaded ranges stand about 15 m high, one-sixth of the breadth: Alberti’s minimum.
Related rules
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
Lift the dome on a cylindrical or polygonal drum pierced with windows between the ring of the pendentives and the springing of the dome, to light the centre of the church and to make the dome visible from afar.
drum height ≈ ⅓–1 × its radius (Byzantine); much taller in Russian churches
A column is narrower at the top than at the bottom, but the taller the column the less it should be diminished, because distance already makes its top look smaller.
upper Ø : lower Ø = 5⁄6 (≤15 ft) · 11⁄13 (15–20 ft) · 6⁄7 (20–30 ft) · 13⁄15 (30–40 ft) · 7⁄8 (40–50 ft)
Columns may be spaced 1½ diameters apart (pycnostyle), 2 (systyle), 2¼ (eustyle), 3 (diastyle) or more (araeostyle). The eustyle, with a wider central bay of 3 diameters, is the best for use and beauty.
clear space = 1½ · 2 · 2¼ · 3 · >3 D
Divide the whole front of the cornice into nine parts; give one of them to the height of the tympanum, measured at its centre.
tympanum height = cornice width ⁄ 9 (≈ 12½°)
Cite this page Chris Paton, “The piazza as a double square, framed by porticoes”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/alberti-forum-proportion. Text, drawings and models licensed under CC BY-NC 4.0.