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Renaissance mathematics and architectural proportion in Alberti's De re aedificatoria

Published online by Cambridge University Press:  19 August 2008

Lionel March
Lionel March
Affiliation:
School of Arts and ArchitectureUniversity of CaliforniaLos AngelesCalifornia 90032USA
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Abstract

This paper sets Alberti's rules of architectural proportioning in the context of Renaissance mathematical practice. While Alberti makes didactic use of the well developed theories of harmony from music, it is shown that his architectural usage is not analogous to musical systema, even though the arithmetical foundations are shared. The common base for fifteenth-century musical theory and Alberti's architectural recommendations is Pythagorean arithmetic, derived largely from Nicomachus. Alberti also develops a geometrical approach involving magnitudes derived from the cube. Neither the diagonal of a face, nor the diameter of the sphere which circumscribes the cube are commensurable with its side. Alberti makes use of rational estimates for the square roots of two and three, and these ratios are evident in his work. Some examples are indicated for the purpose of linking theory to practice, but it is not the intention of this paper to analyse specific buildings in depth. The purpose of the paper is to suggest a potent theoretical frame within which future empirical investigations might flourish.

Type
Theory
Information
arq: Architectural Research Quarterly , Volume 2 , Issue 1 , Autumn 1996 , pp. 54 - 65
Copyright
Copyright © Cambridge University Press 1996

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References

Ackerman, J. S. (1991). Distance Points: Essays in Theory and Renaissance Art and Architecture, The MIT Press, Cambridge, MA.Google Scholar
Alberti, L. B. (1980). Ludi matematici, Ugo Editore, Milan (original title Ludi rerum matematicarum) from Cecil Grayson's edition Alberti: Opere volgari (volume III), Laterza.Google Scholar
Alberti, L. B. (1972). On Painting and On Sculpture, edition and translation of De pictura and De statua by Grayson, Cecil, Phaidon Press, LondonGoogle Scholar
Alberti, L. B. (1988). On the Art of Building in Ten Books, translation of De re aedificatoria by Rykwert, Joseph, Leach, Neil, Tavernor, Robert, The MIT Press, Cambridge, Massachusetts.Google Scholar
Barker, A. (1989). Greek Musical Writings, Volume II. Harmonic and Acoustic Theory, Cambridge University Press, Cambridge.Google Scholar
Baxandall, M. (1972). Painting and Experience in Fifteenth Century Italy, Oxford University Press, London.Google Scholar
Boethius, (1967). De institutione musica. For a translation see Bower, Calvin: Boethius' The Principles of Music an Introduction, Translation, and Commentary. PhD Thesis, University Microfilm, Ann Arbor, Michigan.Google Scholar
Boethius, (1983). Boethian Number Theory, a translation into English by Masi, Michael, Rodopi, Amsterdam.Google Scholar
Borsi, F. (1977). Leon Battista Alberti, Phaidon, Oxford.Google Scholar
Burns, H. (1979). ‘A drawing by L. B. Alberti’, Architectural Design, 49, 5–6, pp. 45–56.Google Scholar
Cajori, F. (1928). A History of Mathematical Notation, The Open Court Publishing Company, La Salle, Illinois.Google Scholar
Cornford, F. (1937). Plato's Cosmology, Routledge & Kegan Paul, London.Google Scholar
Davis, M. D. (1977). Piero della Francesca's Mathematical Treatises, Longo Editore, Ravenna.Google Scholar
Elders, W. (1991). Composers of the Low Countries, Clarendon Press, Oxford.Google Scholar
Flegg, G., Hay, C., Moss, B. editors (1985). Nicolas Chuquet, Renaissance Mathematician, D. Reidel, Dordrecht.Google Scholar
Fowler, D. (1987). The Mathematics of Plato's Academy: A New Reconstruction, Clarendon Press, Oxford.Google Scholar
Gadol, J. (1973). Leon Battista Alberti: Universal Man of the Early Renaissance, The University of Chicago Press, Chicago and London.Google Scholar
Gaffurius, F. (1977). De harmonia musicorum instrumentorum opus, introduction and translation, Miller, Clement A, American Institute of Musicology.Google Scholar
Heath, T. L. (1956). The Thirteen Books of Euclid's Elements, Dover Publications, New York.Google Scholar
Heath, T. L. (1928). A History of Greek Mathematics, Clarendon Press, Oxford.Google Scholar
Herz-Fischler, R (1987). A Mathematical History of the Division in Extreme and Mean Ratio, Wilfred Laurier University Press, Waterloo, Ontario.Google Scholar
Mancini, G. (1911). Vita di Leon Battista Alberti, Florence.Google Scholar
Nicomachus of Gerasa (1938). Introduction to Arithmetic, translated from the Greek by D'Ooge, Martin Luther, with studies in Greek arithmetic by Robbins, Frank Egleston and Karpinski, Louis Charles, University of Michigan Press, Ann Arbor.Google Scholar
Pacioli, L. (1509). Divina Proportione, Venice.Google Scholar
Palisca, C. V. (1985). Humanism in Italian Renaissance Musical Thought, Yale University Press, New Haven.Google Scholar
Rose, P. L. (1975). The Italian Renaissance of Mathematics, Libraire Droz, Genève.Google Scholar
Rykwert, J., Tavernor, R. (1979). ‘Church of S. Sebastiano in Mantua: a tentative restoration’, Architectural Design, 49, 5–6, pp. 86–95.Google Scholar
Scholem, G. (1974). Kabbalah, Dorset Press, New York.Google Scholar
Tavernor, R. (1979). ‘Reconstruction drawings for S Sebastiano’, Architectural Design, 49, 5–6, pp. 76–85.Google Scholar
Tavernor, R. (1985). Concinnitas in the Architectural Theory and Practice of L. B. Alberti, PhD Thesis, University of Cambridge.Google Scholar
Taylor, T. (1983). The Theoretic Arithmetic of the Pythagoreans, Samuel Weiser, York Beach, Maine, first published in London in 1816.Google Scholar
Theon of Smyrna (1979). Mathematics Useful for Understanding Plato, translated from a French edition by Robert, and Deborah, Lawlor, Wizard Bookshelf, San Diego.Google Scholar
Vitruvius, (1931). De architectura, translated by Granger, Frank, Harvard Universtity Press, Cambridge, Massachusetts.Google Scholar
Waterfield, R., translator (1988). The Theology of Arithmetic, Phanes Press, Cedar Rapids, Michigan.Google Scholar
Wittkower, R. (1988). Architectural Principles in the Age of Humanism, Academy Editions, London.Google Scholar