The history of Western architecture is marked by ample attention to the concept of proportion, a concern that has affected both architectural theory (ever searching for aesthetic recipes for harmony) and architectural practice (seeking to balance loads and structure). In fact, the term proportion expresses a quantitative relationship between measurable elements and is therefore intrinsic to the geometric forms commonly employed in building designs. According to Western classical traditions, humans have always aspired to the perfection of natural forms; this helps to explain the enduring fascination with proportional systems in architectural design.

For a long time, geometry and proportion represented secret and sacred tools that assured formal coherence and structural balance. Through them, early modern thinkers such as Galileo sought to establish the foundations of experimental science and to demonstrate thresholds of validity for structural principles. According to Goethe's famous aphorism, “Provision has been made to keep trees from growing up into the sky”—in other words, there is a rational limit to all things.1

Given the significance ascribed to proportion by so many for so long, it is not surprising that architectural debates continue to explore the multiple implications of proportion for the history and theory of design. The invention of new design technologies has also drawn renewed attention to the theme, reviving interest in the generative algorithms of “visual design” and the ways in which these are controlled by geometry, and therefore proportion.

The study of architectural proportion systems employed in the classical world and during the Renaissance boasts a rich and varied international bibliography. Such research flourished in particular just after World War II, most notably with the publication in 1949 of Rudolf Wittkower's landmark Architectural Principles in the Age of Humanism, a book long credited with awakening the interest of architectural historians in the topic. This was followed in 1958 by Peter Scholfield's The Theory of Proportion in Architecture. In the period between these two books, in 1951, Anna Cimoli and Fulvio Irace organized “De Divina Proportione” in Milan; this major international conference on architectural proportions brought together some of the most prominent architects, historians, and critics of the time, including Wittkower, Sigfried Giedion, James Ackerman, Bruno Zevi, Matila Ghyka, Pier Luigi Nervi, and Le Corbusier.2 Matthew A. Cohen and Maarten Delbeke's important edited volume Proportional Systems in the History of Architecture now brings this discussion into the twenty-first century. The book consists of articles originally published from 2014 to 2016 as part of a series in the journal Architectural Histories that followed from an international conference (also titled “Proportional Systems in the History of Architecture”) held in Leiden in 2011 to commemorate the sixtieth anniversary of “De Divina Proportione.” Cohen and Delbeke's book thus takes part in an ongoing debate regarding architectural proportions that extends across time and has attracted the attention of both academics and practitioners.

A signal contribution of this new book is its presentation of several key original sources, including an English translation by Caroline van Eck of an unpublished 1933 essay by Wittkower, “The Problem of Movement in Mannerist Architecture”; some short writings by Le Corbusier presented by Jean-Louis Cohen in his study of Le Corbusier's Modulor; and a transcription of Matthew Cohen's interview with James Ackerman, the last living participant of the 1951 conference. The conversation with Ackerman explores different approaches to the study of proportional systems and establishes a strong link between the 1951 and 2011 conferences by assessing the legacy of Wittkower, Le Corbusier, and Colin Rowe. It concludes with reflections on the future of proportional systems as related to digital design practice.

Framed by an introduction and a conclusion by Matthew Cohen, the essays contained in the book enable readers to better understand the potential of architectural proportional systems in terms of their relevance for computer-aided design and their impact on the history and theory of architecture. The book will thus provide an important resource for a wide audience of scholars and practitioners. In his introduction to Part I, “Two Kinds of Proportion,” Cohen focuses on the debate between those who claim that proportion represents a subjective solution in the search for harmony and those who assert that it offers an objective measure and reference. As Cohen argues, these two antithetical but inseparable extremes inevitably permeate discussions of dimension, composition, and aesthetics. Cohen continues the debate in Part VI, following his interview with Ackerman, where he lists ten fundamental principles for the study of proportional systems in the history of architecture. These principles derive from Cohen's critical reworking of the conclusions proposed by the volume's twenty-two contributing authors.

Part II consists of six chapters that examine theoretical principles in architecture from the classical world to modernity. Mario Curti addresses the unresolved conflict between proportional canons that claim to express natural laws, from the Renaissance to Le Corbusier's Modulor. Caroline van Eck considers the anthropomorphic characteristics of Michelangelo's design for the Laurentian Library vestibule as related to Wittkower's essay on mannerism. Sigrid de Jong explores the question of subjectivity with regard to classical proportions, focusing on eighteenth-century discussions of the anomalous Temple of Neptune in Paestum. Anthony Gerbino discusses the study of proportions in the work of François Blondel in early modern France. Stephen Murray explores the construction of Gothic architecture using digital studies of Beauvais Cathedral, comparing plans and sections to reconstruct geometric proportions. Marvin Trachtenberg closes the section with an essay on Wittkower's study of the role of perspective in shaping Filippo Brunelleschi's design practice and Renaissance theories of architectural proportion.

Part III considers proportion as a design tool and its relationship to modules and modular grids. Eight chapters span the history of architecture from the classical world to the dawn of the Enlightenment. Elizabeth den Hartog explains the symbolism of numbers in early Gothic constructions. Lex Bosman contextualizes the role of the module from Vitruvius through Italian Renaissance treatises. Mark Wilson Jones tackles measurement and the design logic of the Parthenon. Franco Barbieri examines Vincenzo Scamozzi's proposals for the correct dimensioning of rooms. Krista De Jonge investigates the significance of proportion for early modern Flemish artists and architects as seen in prints. Konrad Ottenheym illustrates the application of proportional systems in Dutch civil architecture. Jeroen Goudeau explains the use of the modular grid as a design tool in early nineteenth-century France. Finally, Robert Bork provides an original reading of design strategies in Gothic architecture, demonstrating how geometric matrices formed a key element in design practices.

Part IV documents how sets of data provided by new analytical tools enable scholars to reassess earlier studies and conclusions, underscoring the value and effectiveness of digital representations for the study of architecture. Andrew Tallon describes the application of laser scanning to the study of the proportions of Bruges Cathedral. Gerd Graßhoff and Christian Berndt analyze entasis in the columns of the Pantheon portico. Francesco P. Di Teodoro explains the role of proportions in Leonardo da Vinci's drawings of religious buildings. Sara Galletti examines the chronology of Philibert de l'Orme's treatise in light of his changing ideas about proportions. Maarten Delbeke considers Claude Perrault's rejection of proportion as an aesthetic rule.

Part V comprises three chapters that explore theoretical interpretations of proportion. Jean-Louis Cohen approaches the debate around proportional systems in twentieth-century France by investigating Le Corbusier's reliance on the theoretical studies of Matila Ghyka for his Modulor measurements. Caroline Voet illustrates the refined proportional principle behind the Belgian Benedictine monk Hans van der Laan's plastic number, which anticipated the parametric logic of solid modeling. Finally, Francesco Benelli investigates the argument between Wittkower and Le Corbusier that stirred backstage at the 1951 conference.

With its distinguished list of contributors, this large and impressive book deserves careful reading. It offers a series of well-articulated perspectives on proportional systems across time and space and raises provocative questions. Persistent, centuries-old debates around proportion have reappeared in the new millennium. The rise of digital technology, contributing to this resurgence, offers yet another means through which scholars can understand and investigate the value and significance of proportional systems.



“Es ist dafür gesorgt, daß die Bäume nich in den Himmel wachsen.” Quoted in A. D'Arcy Wentworth Thompson, On Growth and Form (Cambridge: Cambridge University Press, 1917), 20. Johann Wolfgang von Goethe, Goethe's Collected Works, trans. Robert R. Heitner (New York: Suhrkamp, 1987), 4:333.


Tensions between Wittkower and Le Corbusier, both of whom claimed to have rediscovered classical proportional theory in architecture, are well documented. For a discussion of Wittkower's impact on modernist architecture, see Alina Payne, “Rudolf Wittkower and Architectural Principles in the Age of Modernism,” JSAH 53, no. 3 (Sept. 1994), 322–42.