I “PRONTUARI” ELLENISTICI E IL PROGETTO ARCHITETTONICO NEL MONDO ANTICO

The aim of this research is to present the results of studies on the numerical and geometric problems underlying ancient architectural design, achieved through the integration of various literary sources. By employing digital surveying techniques to create updated documentation of ancient buildings, and by integrating new insights from the critical editions of ancient mathematical texts edited by Johan Ludvig Heiberg, we have deepened our understanding of key examples of architectural production from the 2nd century CE. The surviving fragments of what can be considered practical handbooks assist contemporary scholars in understanding how complex computational problems were solved by ancient architects. The computational problems had to be reconciled with modular grids and geometric schemes based on figurative motifs. The practical nature of the texts—collected and analyzed by Heiberg according to the geometric forms of the elements to be calculated—opens new avenues of research for architectural historians. Heiberg’s texts reveal a previously overlooked and complementary perspective to that of Vitruvius, who deliberately operates on a theoretical level and avoids addressing purely computational topics. In De Architectura, numerical examples or distribution schemes (distributio) are absent, as the text aims to elevate the status of the architect by emphasizing geometric constructions and modular patterns, as exemplified by the graphical algorithm of the theatre. It is noteworthy that Heiberg attributes much of this corpus of formulas to Hero of Alexandria, although there remains considerable uncertainty regarding the actual authorship of them, which are substantially different from those of the classical golden age of Greek geometry and mathematics (e.g., Euclid, Archimedes, and Apollonius). Thanks to the contributions of Hero’s texts—rich in numerical examples that are not abstract but fully aligned with constructive logic—it is possible to retrace the phases of ancient architectural design, starting from the most complex structural elements such as arches, domes, niches, and curved surfaces in vaulted systems.