Proportional Systems in the History of Architecture
Proportional Systems in the History of Architecture
A Critical Consideration
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Table of Contents
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I. Introduction
Chapter 1: Two Kinds of Proportion (Revised)
Matthew A. Cohen
II. Thinking and Seeing Proportion
Chapter 2: Canons of Proportion and the Laws of Nature: Observations on a Permanent and Unresolved Conflict
Mario Curti
Chapter 3: The Composto Ordinato of Michelangelo’s Biblioteca Laurenziana: Proportion or Anthropomorphy?
Caroline van Eck
Appendix: The Problem of Movement in Mannerist Architecture (1933), by Rudolf Wittkower. Translated by Caroline van Eck.
Chapter 4: Subjective Proportions: 18th-Century Interpretations of Paestum’s “Disproportion”
Sigrid de Jong
Chapter 5: Were Early Modern Architects Neoplatonists? The Case of François Blondel
Anthony Gerbino
Chapter 6: Plotting Gothic: A Paradox
Stephen Murray
Chapter 7: To Build Proportions in Time, or Tie Knots in Space? A Reassessment of the Renaissance Turn in Architectural Proportions
Marvin Trachtenberg
III. Designing with Proportion
Chapter 8: 1, 2, 3, 6: Early Gothic Architecture and Perfect Numbers Elizabeth den Hartog
Chapter 9: Proportion and Building Material, or Theory versus Practice in the Determination of the Module
Lex Bosman
Chapter 10: Approaches to Architectural Proportion and the “Poor old Parthenon” (Mark Wilson Jones)
Chapter 11: Scamozzi’s Orders and Proportions: An End to Illusions or a Visionary Harbinger? (Franco Barbieri)
Chapter 12: Early Modern Netherlandish Artists on Proportion in Architecture, or “de questien der Simmetrien met redene der Geometrien” (Krista De Jonge)
Chapter 13: Proportional Design Systems in 17th-Century Holland (Konrad Ottenheym)
Chapter 14: The Matrix Regained: Reflections on the Use of the Grid in the Architectural Theories of Nicolaus Goldmann and Jean-Nicolas-Louis Durand (Jeroen Goudeau)
Chapter 15: Dynamic Unfolding and the Conventions of Procedure: Geometric Proportioning Strategies in Gothic Architectural Design (Robert Bork)
Appendix: The Geometry of Bourges Cathedral
IV. New Approaches to Well-Known Sources
Chapter 16: Divining Proportions in the Information Age (Andrew Tallon)
Chapter 17: Decoding the Pantheon Columns (Gerd Graßhoff) and (Christian Berndt)
Chapter 18: Leonardo da Vinci: The Proportions of the Drawings of Sacred Buildings in Ms. B, Institut de France (Francesco P. Di Teodoro)
Chapter 19: Philibert de L’Orme’s Divine Proportions and the Composition of the Premier tome de l’architecture (Sara Galletti)
Chapter 20: An Old Problem? Claude Perrault’s Views on Beauty and Proportion in Architecture and French Aesthetic Theory (Maarten Delbeke)
V. Twentieth-Century Perspectives
Chapter 21: Le Corbusier’s Modulor and the Debate on Proportion in France (Jean-Louis Cohen)
Appendix 1: A Timely Book (1927), by Le Corbusier. Translated by Genevieve Hendricks.
Appendix 2: Regulating Lines (1934), by Le Corbusier. Translated by Matthew A. Cohen and Maarten Delbeke.
Chapter 22: Between Looking and Making: Unravelling Dom Hans van der Laan’s Plastic Number (Caroline Voet)
Chapter 23: Rudolf Wittkower versus Le Corbusier: A Matter of Proportion (Francesco Benelli)
Chapter 24: Proportional Systems in the History of Architecture: A Conversation with James S. Ackerman (James S. Ackerman and Matthew A. Cohen)
VI. Conclusion
Chapter 25: Ten Principles for the Study of Proportional Systems in the History of Architecture (Revised) (Matthew A. Cohen)

Matthew Cohen, Maarten Delbeke (eds)

Proportional Systems in the History of Architecture

A Critical Consideration

In this collection of original essays, twenty-five leading scholars reconsider the long history of proportional systems across numerous periods and places, and from diverse methodological approaches including archival exploration, advanced laser scanning, and more. Prior to the advent of modern structural engineering, architects and builders used proportional systems to imbue their works with a general condition of order that was integral to their intertwined notions of beauty and structural stability. These mostly invisible intellectual frameworks ranged from simple grids and symbolic numbers, to sly manipulations of geometry and numbers that required privileged knowledge and arithmetical calculations to access. Since the origins of architectural history, proportional systems have served as objects of belief and modes of iconographical communication. Whether they are capable of fulfilling more tangible functions remains a matter of debate today, for this ancient and diverse belief system continues to infiltrate architectural thinking in subtle and sometimes surprising ways.

Matthew Cohen

Matthew A. Cohen is a licensed architect and Professor of Architecture at Washington State University. He publishes on the history and theory of medieval and Renaissance architecture. His book, Beyond Beauty: Reexamining Architectural Proportion through the Basilicas of San Lorenzo and Santo Spirito in Florence (Marsilio, 2013), received the 2012 James Ackerman Award in the History of Architecture.

Maarten Delbeke

Maarten Delbeke is Chair in the History and Theory of Architecture at the Institute for the History and Theory of Architecture (gta) at the ETH in Zürich. He publishes on the history and theory of art and architecture from the early modern period up to the present and is an architecture critic, and is the founding editor of Architectural Histories.