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

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.