Geometry and equilibrium: The gothic theory of structural design

Abstract

Medieval builders didn't have a scientific structural theory, however gothic cathedrals were not build without a theory. Gothic masters had a ‘scientia' and this scientia was firmly based in geometry. It is the form which guarantees a safe state of equilibrium.
In many gothic sources we find rules to design the structural elements, with special emphasis in buttress design. These rules lead in most cases to a a proportional design, independent of scale (the depth of a buttress as a fraction of the span). The late-gothic Spanish architect Rodrigo Gil formulated arithmetical rules which lead to non-proportional designs (the buttresses become more slender as the general size grows).
Gothic structural rules were a means to register stable forms. Proportional rules are essentially correct and apply to most cases. Rodrigo Gil's rules express a finer adjustment to some non-proportional problems: buttress design for thin late-gothic vaults or wall design for towers.