From empirical engineering to science-based engineering: the assessment by three mathematicians of the “San Pietro” dome (1742)

The studies on the mechanic behaviour of domes, based on the static analysis of arches and vaults, started in the first half of the XVII century. At the end of 1741, when the Pope Benedetto XIV commissioned an assessment to three mathematicians Roger Joseph Boscovich, François Jacquier e Thomas Le Seur, belonging to the Repubblica Romana dei dotti. There where serious worries on the static conditions of the San Pietro vault where important cracks could be appreciated. Some interesting studies were developed on this problem, even followed by learned and heated arguments, that lead to compile treatises that systemized the knowledge on this argument. The historical documents even report the opinion of other experts, for example that one of the mathematician Giovanni Poleni from Padua. On spite of that, the study of the three previous mathematicians was different from the others carried out before because it had an important innovation: the assessment was accomplished, perhaps for the first time, using a scientific criterion in order to interpret the mechanic behaviour of an architectural structure. Its historical importance resides on the scientific theoretical conceptions used to analyze a structural problem that were completely different from the empirical rules, at most of geometric nature, used before. The principle of virtual works was further applied in the assessment. It was used to define the size of the metal rings for the drum of the vault. Some researchers intend this assessment as the moment when the change from the engineering based on artisan traditions to the engineering based on the application of new scientific theories has been accomplished