ESHS/HSS Annual Meeting

Mathematical Knowledge in Premodern Atlantic Iberian Carpentry Traditions

• In Event: Practitioners, Artisans and Instruments in the Making of Premodern Science, II

English Abstract

In this paper, I present the circulation and rhetorical deployment of mathematical knowledge within the Spanish carpintería de lo blanco and its colonial extensions, arguing that Euclidean and Archimedean traditions were mobilized as instruments of professional legitimation rather than straightforward operational recipes. Focusing on Diego López de Arenas' Breve compendio (1633) and a previously understudied manuscript by Fray Andrés de San Miguel in New Spain, I trace how canonical propositions—Euclid’s semicircle theorem and Archimedes’ quadrature—were transformed into graphic, compass and rule procedures for producing cartabones and for rectifying circumferences in dome construction. Close reading of manuals, guild ordinances, and examination practices shows that municipal and colonial corporations institutionalized geometric competence through categories such as jumétrico and lazero, embedding geometry within regulatory and pedagogical frameworks. López de Arenas' printed compendium performs a guild centered rhetorical project aimed at policing standards and restoring alarife authority, while San Miguel’s manuscript systematizes compass and polygon based techniques within monastic and colonial pedagogies. Together they reveal a shared geometrical repertoire that circulated across the Iberian Atlantic but whose routine operational uptake on building sites remains empirically unresolved.

Author

• Sebastián Molina-Betancur, Independent scholar