Transfer of Mathematical Knowledge for Building Medieval Cathedrals

Abstract

The construction of Gothic cathedrals is among the great achievements of medieval science, as defined in terms of theorica and practica. The success of these constructions is due to the knowledge of promoters and builders. This study introduces the original sources of the codex of the cathedral of Tortosa (Catalonia, Spain) with authors such as Calcidius, Capella, Macrobius, Al-Ḣ ajjāj ibn Yūsuf ibn Mat˙ar or Gerbert. The combined assessment of these sources, together with the masonry built and Guarc's original plan (c.1345-c.1380) shed some light on the mathematical knowledge of the cathedrals' builders. Keywords Mathematics in middle ages • Gothic cathedrals • Medieval geometry • Heptagon • Octagon • Tortosa cathedral Abbreviations ACTo Arxiu capitular tortosa (Chapter Archives of Tortosa) AHCTE Arxiu històric comarcal terres ebre FBMPM Fundación bertomeu march palma mallorca

El trazado geométrico del ábside del gótico meridional de la catedral de Tortosa.

“…En ambos casos el texto se ilustra con tres figuras que indican las secuencias numéricas que dan lugar a las relaciones tonales del Timeo (Tim. 35B-36B) (15). El peso de la tradición tardo clásica en el Sur de Francia, Italia y el Levante español, hizo intuir a Viollet-le-Duc la utilización de proporciones diferentes frente a los modelos septentrionales (5).…”