Geometry and Design in Palladio's Architecture

Andrea Palladio (1508–80) is among the most loved and influential of the architects of the Italian Renaissance, famous for his elegantly proportioned buildings and for his treatise on architecture, the Quattro Libri dell'Architettura, first published in Venice in 1570. However, in terms of our understanding of exactly how Palladio achieved his ‘elegantly proportioned’ results, surprisingly little is known.

Palladio does say that good proportions are very important, but he never explains his own methods, nor any more general theory of design. What Palladio does instead is to present us with a set of examples. The Quattro Libri as it stands is a collection of these examples, ancient and modern, some built and some not.

Many attempts have been made to decode Palladio's system, the most influential of which remains Wittkower's treatment in his book Architectural Principles in the Age of Humanism(1949). Wittkower's harmonic proportions hypothesis has fallen out of favour, but the more fundamental questions Wittkower poses have not gone away.

Key Findings

This dissertation identifies the geometric basis of Palladio's design method. First, it shows that the equilateral triangle, and its related forms, was integral to his design process — indeed it was ubiquitous. Recognising this allows us to move past the limitations of previous analyses which have viewed his designs using the framework of a two-dimensional Cartesian grid.

Relationships which were previously overlooked become obvious, such as those based on the ratio of an equilateral triangle's base to its height: 1: √3/2.

Secondly, this dissertation demonstrates that an understanding of Palladio's use of these specific proportions, and the numerical ratios used to approximate them, makes interpreting his designs straightforward. Once we are familiar with Palladio's number systems, we can explain his marked dimensions and his unmarked dimensions.

Structure

• Chapter 1 — Palladio's use of geometry and his ancient, medieval, and contemporary sources.
• Chapter 2 — The geometry primer, including a look-up table of number systems.
• Chapter 3 — Application to architecture: shortcuts, typologies, elevation, plan, and three dimensions.
• Chapters 4–7 — Case studies across four classes: the five orders, Vitruvian temple types, Palladio's own buildings, and ancient Roman reconstructions.

Keywords