The late gothic ribbed vaults of San Miguel church in Segovia: from geometric and proportional analysis to structural assessment

Abstract Rodrigo Gil de Hontañón’s treatise represents a remarkable codification of the empirical scientia underlying late Gothic church design, providing geometric-proportional and construction rules. Although these design criteria have been extensively investigated from a historical perspective, they have only rarely been verified through a systematic comparison with buildings designed by Rodrigo Gil himself, nor have such structures been analyzed using contemporary methods for structural assessment. This paper addresses these issues through the study of the Church of San Miguel in Segovia, designed by Rodrigo Gil, combining historical and geometric investigation, and structural analysis. The geometric-proportional rules described in the treatise are first reconstructed and compared with the geometry derived from laser scanner and photogrammetric surveys, allowing the ideal design geometry to be distinguished from construction adaptations and subsequent deformations. The comparison reveals a remarkable correspondence between the proportional system described in the treatise and the surveyed geometry of the church, confirming the application of Rodrigo Gil’s design principles. The main ribbed vault is then investigated through membrane equilibrium analysis and thrust-line analysis of the tiercerons, showing that the reconstructed geometry is consistent with mechanically admissible equilibrium configurations, and therefore demonstrating that these empirical rules reflected a coherent structural conception rather than merely formal geometric prescriptions. Beyond the specific case of San Miguel, the study demonstrates how the integration of historical treatises, digital survey and structural analysis can contribute to interpreting the scientia underlying late Gothic masonry design.