Robin Evans recasts the idea of the relationship between geometry and architecture, drawing on mathematics, engineering, art history, and aesthetics to uncover processes in the imagining and realizing of architectural form. Anyone reviewing the history of architectural theory, Robin Evans observes, would have to conclude that architects do not produce geometry, but rather consume it. In this long-awaited book, completed shortly before its author's death, Evans recasts the idea of the relationship between geometry and architecture, drawing on mathematics, engineering, art history, and aesthetics to uncover processes in the imagining and realizing of architectural form. He shows that geometry does not always play a stolid and dormant role but, in fact, may be an active agent in the links between thinking and imagination, imagination and drawing, drawing and building. He suggests a theory of architecture that is based on the many transactions between architecture and geometry as evidenced in individual buildings, largely in Europe, from the fifteenth to the twentieth century. From the Henry VII chapel at Westminster Abbey to Le Corbusier's Ronchamp, from Raphael's S. Eligio and the work of Piero della Francesca and Philibert Delorme to Guarino Guarini and the painters of cubism, Evans explores the geometries involved, asking whether they are in fact the stable underpinnings of the creative, intuitive, or rhetorical aspects of architecture. In particular he concentrates on the history of architectural projection, the geometry of vision that has become an internalized and pervasive pictorial method of construction and that, until now, has played only a small part in the development of architectural theory. Evans describes the ambivalent role that pictures play in architecture and urges resistance to the idea that pictures provide all that architects need, suggesting that there is much more within the scope of the architect's vision of a project than what can be drawn. He defines the different fields of projective transmission that concern architecture, and investigates the ambiguities of projection and the interaction of imagination with projection and its metaphors.

Conversant in contemporary theory and architectural history, Stan Allen argues that concepts in architecture are not imported from other disciplines, but emerge through the materials and procedures of architectural practice itself. Drawing on his own experience as a working architect, he examines the ways in which the tools available to the architect affect the design and production of buildings. This second edition includes revised essays together with previously unpublished work. Allen’s seminal piece on Field Conditions is included in this reworked, revised and redesigned volume. A compelling read for student and practitioner alike.

This important book, which won the 1984 Alice Davis Hitchcock Award, traces the process by which the mystical and numerological grounds for the use of number and geometry in building gave way to the more functional and technical ones that prevail in architectural theory and practice today. Between the late Renaissance and the early nineteenth century, the ancient arts of architecture were being profoundly transformed by the scientific revolution. This important book, which won the 1984 Alice Davis Hitchcock Award, traces the process by which the mystical and numerological grounds for the use of number and geometry in building gave way to the more functional and technical ones that prevail in architectural theory and practice today. Throughout, it relates the major architectural treatises of successive generations to the larger culture and the writings of philosophers, mathematicians, scientists, and engineers. The book leads the reader through the controversy that was generated by Claude Perrault in the seventeenth century. His writings began to cast doubt on the absolute aesthetic value of the classical orders and the "perfect" proportions that were architecture's legacy from Pythagorean times. Thus the once immutable "invisible" system lost its special status forever. The book focuses in particular on eighteenth-century developments in the science of mechanics and emerging techniques in structural analysis which slowly entered the architectural treatises and found their way into practice, often by way of civil and military engineers. And by the nineteenth century, the book notes, even architectural rendering and drawing were radically changed through the introduction of new descriptive and projective geometries. Tracing these fundamental changes in architectural intentions, Pérez-Gómez challenges many popular misconceptions about the theory and history of modern architecture. At the same time, he suggests an intangible loss, that of a culture's power to express through a building its total mathematical, mystical, and magical world-view.

For more than half a century, Erwin Panofsky's Perspective as Symbolic Form has dominated studies of visual representation. Despite the hegemony of central projection, or perspective, other equally important methods of representation have much to tell us. Parallel projection can be found on classical Greek vases, in Pompeiian frescoes, in Byzantine mosaics; it returned in works of the historical avant-garde, and remains the dominant form of representation in China. In Oblique Drawing, Massimo Scolari investigates "anti-perspective" visual representation over two thousand years, finding in the course of his investigation that visual and conceptual representations are manifestations of the ideological and philosophical orientations of different cultures. Images prove to be not just a form of art but a form of thought, a projection of a way of life. Scolari's generously illustrated studies show that illusionistic perspective is not the only, or even the best, representation of objects in history; parallel projection, for example, preserves in scale the actual measurements of objects it represents, avoiding the distortions of one-point perspective. Scolari analyzes the use of nonperspectival representations in pre-Renaissance images of machines and military hardware, architectural models and drawings, and illustrations of geometrical solids. He challenges Panofsky's theory of Pompeiian perspective and explains the difficulties encountered by the Chinese when they viewed Jesuit missionaries' perspectival religious images. Scolari vividly demonstrates the diversity of representational forms devised through the centuries, and shows how each one reveals something that is lacking in the others.

This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory, and many other related topics, with an emphasis on the subject's novel, striking aspects. 1955 edition.

In his writings, Hume talks of our 'gilding and staining' natural objects, and of the mind's propensity to 'spread itself' on the world. This has led commentators to use the metaphor of 'projection' in connection with his philosophy: Hume is held to have taught that causal power and self are projections, that God is a projection of our fear, and that value is a projection of sentiment. By considering what it is about Hume's writing that occasions this metaphor, P. J. E. Kail spells out its meaning, the role it plays in Hume's work, and examines how, if at all, what sounds 'projective' in Hume can be reconciled with what sounds 'realist'. In addition to offering some highly original readings of Hume's central ideas, Projection and Realism in Hume's Philosophy offers a detailed examination of the notion of projection and the problems it faces.