On Vaulting: Heron’s Manuals and Their Role in Roman Dome Design

The subject of domes in the Roman world is complex and can be studied from different perspectives. In this paper we focus on the relationship between Heron of Alexandria's manuals and the vaulting systems of the Hadrianic age. Our aim is to compare a selection of formulae from the critical edition by Johan Ludvig Heiberg with a series of buildings recently documented using photogrammetric and laser scanner technologies. The collection of writings Heronis Alexandrini opera quae supersunt omnia (mainly books IV and V) presents an interesting set of formulae for calculating vaults and domes: volumes and areas of niches, spherical segments, lunettes, as well as empirical strategies for calculating complex shapes. This approach, which integrates practical knowledge with Vitruvian graphic schemes, allows us to clarify the work of the ancient architect and consequently to investigate the architectural problem within the more general framework of archaeology with new conceptual tools.