Geometrical proportioning of masonry arch bridges

The design of masonry arches has been based for centuries on empirical rules, and many of the arch bridges currently in use were designed and built ac-cording to geometric proportions. All the elements of the bridge, thickness at the springer and at the crown, dimensions of the abutments, height of the abut-ments, were defined according to methods that were reported for the first time in Renaissance treatises. The structure of geometric relations took on increas-ingly complex forms in relation to the development of mathematical thought of the time. This article presents a reasoned catalogue of empirical formulas re-ported in treatises from the Renaissance to the first decades of the twentieth century, together with an evaluation of their reliability using modern calcula-tions.