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 · Columns · Proportion · Theory
The five orders as a series
Rank the orders in a sequence from the plainest and strongest to the richest and most slender (Tuscan, Doric, Ionic, Corinthian, Composite), each one diameter taller than the last.
6 · 7 · 8 · 9 · 10 D
Serlio’s woodcut of the five orders side by side, like a family photograph in order of height, was new: Vitruvius described only four orders, and never as a series. The idea that the orders form a scale (of strength, richness and “character”) became fundamental: Tuscan for fortresses and prisons, Doric for soldiers and heroes, Ionic for scholars and matrons, Corinthian for virgins and the Virgin.
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
Give the flight of steps before a temple an odd number, so that one who starts with the right foot will also set the right foot first on the top.
Every building must satisfy three demands at once: it must stand up (firmitas), serve its purpose (utilitas), and give pleasure to the eye (venustas).
architecture = firmitas + utilitas + venustas
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)
Keep the lowest third of the shaft cylindrical; above it, reduce the radius along a curve found by dividing a quarter-circle and the upper two-thirds of the shaft into the same number of equal parts.
r(k) = R · cos(α·k), cos α = r_top ⁄ R, k = 0…1 over the upper ⅔
Cite this page Chris Paton, “The five orders as a series”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/serlio-five-orders. Text, drawings and models licensed under CC BY-NC 4.0.