Chapter 4
The Five Orders
Palladio's treatment of the five orders of architecture in Book I of the Quattro Libriprovides the clearest demonstration of his geometric method. Each order's proportions — column height, entablature depth, intercolumniation — are governed by the equilateral triangle and its key ratio, 1 : √3/2.
The module system Palladio uses (where the column diameter serves as the base unit) creates a framework in which the equilateral triangle generates the proportional relationships between parts. The Tuscan order at 7 modules and the Doric at 8 modules use the 7:6 approximation of √3/2, while the taller orders embed the ratio in more complex ways.
Use the interactive diagram below to explore each order's proportions and see how the triangle overlay reveals the underlying geometric logic.
The Five Orders
Column height: 7 modules
Entablature: 1.75 modules
Total: 8.75 modules
Height × √3/2: 7.578
The simplest order. Palladio's Tuscan column height of 7 modules produces a height-to-diameter relationship governed by the equilateral triangle.
Key Findings
Module Heights
The progression from Tuscan (7) to Composite (10) modules is not arbitrary — each step maintains or refines the equilateral triangle relationship between column height and its design envelope.
Entablature Ratios
Entablature heights consistently approximate 1/4 of column height across all five orders, a ratio that emerges naturally from the equilateral triangle's subdivision properties.
The 7:6 Approximation
Palladio's most frequently used rational approximation of √3/2. It appears explicitly in the Tuscan and Doric orders and implicitly throughout his dimensional specifications.
Intercolumniation
Column spacing follows the same geometric logic — the distance between columns relates to their height through equilateral triangle proportions.