expands the range of possible prototypes to include not only Tuscan and Roman sources but also Gothic-style models from Lom- bardy. His discussion of Lombard models, including Milan Cathedral, San Petronio, Bologna, and especially Santa Maria del Carmine, Pavia, is particularly strong and provides an important contribution to a growing scholarly awareness of regional influences beyond Florence and Tuscany. The second part of the chapter turns to the model of Santa Maria del Fiore in Florence. Cohen’ s new survey of the cathedral reveals key dimensions whose patterns imply a proportional system, one that could have provided the “seed numbers” for the pro- portions used in both San Lorenzo and Santo Spirito (239). Yet, encountering sig- nificant irregularities, he also explores a dif- ferent approach to precision in the medieval period and further investigates number theory in the following chapter. Chapter 6 returns to the book’ s opening premise and to several aspects of Wittkower’ s arguments. Where Wittkower found stark period distinctions, Cohen, in emphasizing both a medieval interest in number and an enduring Renaissance reliance on geometry, instead identifies continuities. The develop- ment of fractional arithmetic was, neverthe- less, a Renaissance innovation, marking a significant turn toward greater precision. Cohen engages recent scholarship, including that of Alfred Crosby and Lon Shelby, that recognizes the significance of applied mathe- matics as a point of intersection between theoreticians and practitioners, important both for advancing mathematical knowledge and for introducing complexity into architec- tural design. Cohen seeks a broad understanding of the mathematical qualities of San Lorenzo’ s design. Medieval and Renaissance observ- ers believed, he argues, that proportional systems could visually symbolize order and represent both strength and beauty. He ad- vances an important proposal for the place of proportions in an age before structural calculations. Understood to convey struc- tural stability, proportional systems played a rhetorical rather than functional role, serving as “invisible bearers of meaning and objects of belief” (275). Cohen then dwells further on his own methodology, which draws upon the disciplines of archaeology, art history, and architectural history. He situates his observation-based research as a rebuttal to Wittkower’ s inattention to the object. This would be a strong conclusion to the book, but Cohen includes an epi- logue in which he reiterates his argument against connecting proportional systems and beauty, and he rebukes modern ob- servers for maintaining an illogical, mys- tical belief in the aesthetic qualities of proportions. True to the book’ s title, Cohen’ s primary subject is architectural proportion. The author presumes a readership already well informed about San Lorenzo’ s history or ready to set aside many attendant issues, such as the construction chronology and the role of patronage. The book’ s structure requires patience, since, particularly with his meticulous analysis of dimensions, Cohen often reveals the direction of his arguments only at their conclusion. Not all aspects of the book equal the rigor of its metrical anal- ysis. Cohen makes plain his reliance on ear- lier scholarship, but the historiographical context is not always clear; a lack of publi- cation dates in the notes challenges the reader’ s ability to understand how the schol- arly arguments have unfolded. A four-page appendix offers measured drawings of San Lorenzo and the Old Sacristy; however, the website offering Cohen’ s comprehen- sive survey results for San Lorenzo and Santo Spirito is inaccessible due to an out- dated URL. Cohen’ s rigorous and focused study sug- gests both the merits and the challenges of his methodology. His close attention to me- dieval and Renaissance mathematics brings added nuance to traditional periodization, contributes to a growing area of research, and offers important insights into the role of mathematics in early Renaissance design while enhancing our understanding of ma- jor monuments in the history of Florentine architecture. ANN C. HUPPERT University of Washington Notes 1. Rudolf Wittkower, Architectural Principles in the Age of Humanism (London: Warburg Institute, 1949); Rudolf Wittkower, “Brunelleschi and ‘Pro- portion in Perspective,’” Journal of the Warburg and Courtauld Institutes 16 (1953), 275–91. 2. The James Ackerman Award, administered by the Centro Internazionale di Studi di Architettura Andrea Palladio, recognizes excellence in the first book by a young scholar in architectural history. 3. Howard Burns, “Building against Time: Renais- sance Strategies to Secure Large Churches against Changes to their Design,” in L ’eglise dans l’architec- ture de la Renaissance, ed. Jean Guillaume (Paris: Picard, 1995), 107–31; Marvin Trachtenberg, Building-in-Time: From Giotto to Alberti and Modern Oblivion (New Haven, Conn.: Yale University Press, 2010). Roberto Gargiani Concrete from Archeology to Invention 1700–1769: The Renaissance of Pozzolana and Roman Construction Techniques Lausanne, Switzerland: École Polytechnique Fédérale de Lausanne (distributed by Routledge), 2013, 404 pp., 300 color and 16 b/w illus. $115.95, ISBN 9782940222643 This book is part of a series titled Treatise on Concrete, which is edited by Roberto Gargiani and published by his university, the École Polytechnique Fédérale de Lausanne. Concrete from Archeology to Invention 1700– 1769, authored by Gargiani, is the first of a group of works within the series that focus on the development of concrete during the eighteenth and nineteenth centuries in Europe. In the preface, Gargiani states that the book’ s goal is to document the evolution of construction techniques through archival research. Indeed, he presents a tremendous amount of material from treatises, old jour- nals, personal letters, and state entities that are otherwise not easily accessible. In fact, large portions of the text consist of quota- tions (translated into English) from the ar- chival sources. On the one hand, this is a useful service, but on the other, any sort of narrative is lost in the minutiae. The author’ s interest in the people who wrote the docu- ments is reflected in his choice to index only proper names and not places or subjects. Nevertheless, the volume contains a wealth of valuable information if one is willing to mine for it. The book begins with an exploration of the period when researchers were trying to discover the secret of the longevity of Roman concrete. Vitruvius’ s treatise offered a starting point, with its formulas for creat- ing hydraulic mortar with pulvis (powder) from the Bay of Naples (Pliny the Elder’ s pulvis Puteolanus, powder from Puteoli— i.e., volcanic ash), but many people at the time believed that ancient craftsmen long before Vitruvius had created a type of myste- rious artificial stone, pierre fondue (11–14). Gargiani notes that developments during the eighteenth century were marked by “an extraordinary mixture of scientific research and fantastic interpretation of sources and BOOKS 501