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Introduction -- Proportion and Continuous Variation in Vitruvius’s De Architectura -- The Palazzo Del Podestà in Bologna: Precision and Tolerance in a Building all’Antica -- Practical Mathematics in the Drawings of Baldassarre Peruzzi and Antonio da Sangallo the Younger -- Geometric Survey and Urban Design: A Project for the Rome of Paul IV (1555–1559) -- Architecture and Mathematics in Early Modern Religious Orders -- The Master of Painted Architecture: Andrea Pozzo, S. J. and His Treatise on Perspective -- Geometry, Mechanics, and Analysis in Architecture -- Epistemological Obstacles to the Analysis of Structures: Giovanni Bottari’s Aversion to a Mathematical Assessment of Saint-Peter’s Dome (1743) -- Scientific Concepts of Beauty in Architecture: Vitruvius Meets Descartes,  Galileo and Newton -- Breathing Room: Calculating an Architecture of Air -- James “Athenian” Stuart and the Geometry of Setting Out -- Index.

This volume explores the mathematical character of architectural practice in diverse pre- and early modern contexts. It takes an explicitly interdisciplinary approach, which unites scholarship in early modern architecture with recent work in the history of science, in particular, on the role of practice in the scientific revolution. As a contribution to architectural history, the volume contextualizes design and construction in terms of contemporary mathematical knowledge, attendant forms of mathematical practice, and relevant social distinctions between the mathematical professions. As a contribution to the history of science, the volume presents a series of micro-historical studies that highlight issues of process, materiality, and knowledge production in specific, situated, practical contexts. Our approach sees the designer’s studio, the stone-yard, the drawing floor, and construction site not merely as places where the architectural object takes shape, but where mathematical knowledge itself is deployed, exchanged, and amplified among various participants in the building process.