Geometry and Design in Palladio's Architecture

Abstract

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. Whether Palladio used a particular geometric or proportional system within his design process, and if so, what precisely that process or system was, remains a subject of intense interest and research. This dissertation aims to significantly advance our understanding of the process that Palladio used to design his buildings. It does this by identifying the geometric basis of his 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. The methods shown allow us to decode Palladio’s designs in plan and in elevation, as a whole and in detail, with orders and without orders, as well as Palladio’s own designs for the five orders, results that were previously out of reach. This dissertation concludes that this method of working was not unique to Palladio. Rather the use of geometric templates, with forms based on the equilateral triangle, was common practice among pre-modern architects. Palladio appears to have developed his own geometric methods based on methods still in use that had survived within the craft techniques of medieval masonry, and which can be traced back, and which Palladio reconnected, to ancient Roman practice. For purposes of comparison, this study also analyses several ancient Roman and medieval designs using these same methods. The examples and methods demonstrated will also be of interest to historians of these periods, to historians of science, and to those interested in the history of knowledge, in particular the craft, metrology, and mathematics used by ancient, medieval, and Renaissance master masons and carpenters. The methods and principles demonstrated may also be of interest to practicing architects, to professors of architectural practice and architectural theory, as well as to those more generally interested in design, and in the history of design. In addition to Palladio, references are made to the methods of Vitruvius, Villard de Honnecourt, Cesare Cesariano, Falconetto, Sebastiano Serlio, Antonio da Sangallo the Younger, Vignola, Vincenzo Scamozzi, and Ottavio Bertotti Scamozzi. The dissertation is divided into two parts. The first half is centred on a geometry primer, followed by selected examples of how Palladio applied his geometry to architecture. The second half provides a comprehensive set of case studies. The primer is designed to introduce the reader, step-by-step, to the fundamental geometric concepts, number systems, and methods used by Palladio. So equipped, the reader will be able to understand, weigh, and evaluate the arguments, evidence, and examples which follow. The reader will also be equipped to examine additional buildings, from any pre-modern period, with respect to the possible presence and usage of such geometries and methods. Chapter 1 introduces Palladio’s use of geometry and considers Palladio’s ancient, medieval, and contemporary sources for such methods. Chapter 2 contains the geometry primer. The primer introduces a look-up table (Appendix 3) to help the reader become familiar with the number systems which Palladio uses hand-in-hand with his geometry. Chapter 3 considers Palladio’s application of his geometric methods to architecture, including his use of short-cuts, and types (typologies), and his approach to design in elevation, in plan, and in three dimensions. Chapter 3 includes an explanation of Palladio’s method of budgeting for wall thicknesses, and the role of the orders within his geometric design system. Chapters 4 to 7 contain case studies. The case study chapters examine and explain Palladio’s use of these methods across four general classes of design problem. These are: (1) Palladio’s designs for the five orders, as published in his own Quattro Libri, (2) Palladio’s designs for Vitruvian ideal temple types, as designed by Palladio for the Barbaro Vitruvius, (3) Palladio’s designs for his own buildings, and (4) Palladio’s reconstructions of ancient Roman buildings.