Geometrical Proportion in the Sixteenth Century: Methods and Constraints

Abstract

Common conceptions about Gothic and Renaissance architectural proportion systems contrast the mediaeval geometrical methods with the arithmetical, rational ones of the Renaissance. In this paper, the authors analyze the geometrical proportion systems in Chapter V of Compendio de Arquitectura y simetría de los templos, generally attributed to the sixteenth-century Spanish architect Rodrigo Gil de Hontañón. This shows that geometrical proportioning system of the Compendio generally leads to rational proportions. However, on some occasions, irrational proportions arise from the geometrical properties of the figures used in the layout of the churches, or from deliberate choices of the author, with a remarkable disregard for the notions of commensurable or incommensurable dimensions. This is consistent with the notion, put forward by Shelby, of constructive geometry. Medieval design methods were based on a compass and ruler geometry, with no concern for rational and irrational proportions.