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 · Proportion · Plans
The seven most beautiful room shapes
Make rooms round, square, or with a length equal to the diagonal of the square, to a square and a third, a square and a half, a square and two-thirds, or two squares.
circle · 1:1 · 1:√2 · 3:4 · 2:3 · 3:5 · 1:2
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
To unify a façade of two or more storeys, run a single order of pilasters or columns through all of them, from the base to the main cornice.
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.
Give the villa garden porticoes for sun and for shade, grottoes made in imitation of nature with tufa and shells, evergreens planted in straight rows at equal distances, and hedges of box; set vines on columns over the walks.
Cite this page Chris Paton, “The seven most beautiful room shapes”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/palladio-room-proportions. Text, drawings and models licensed under CC BY-NC 4.0.