This study examines an ensemble of Romanesque churches in the region of Val d’Aran in the Spanish Pyrenees, built between the 11th and 13th centuries. Seven topographical studies performed between 2014 and 2015 examined these churches systematically using terrestrial laser scanning (TLS) as a data‐acquisition technique. The data obtained allowed for a geometrically accurate analysis of the orientation of these churches based on four Romanesque liturgies: Gemma animae (c.1120), by Honorius of Autun; Rationale divinorum officiorum (c.1150), by Jean Beleth; Mitralis de Officio (1190), by Sicard, Bishop of Cremona; and Prochiron, vulgo rationale divinorum officiorum (1291), by Guillaume Durand.
ABSTRACT:The development of massive data captures techniques (MDC) in recent years, such as the Terrestrial laser Scanner (TLS), raises the possibility of developing new assessment procedures for architectural heritage. The 3D models that it is able to obtain is a great potential tool, both for conservation purposes and for historical and architectural studies. The paper proposes a simple, non-invasive methodology for the assessment of masonry vaults from point clouds which makes it possible to obtain relevant data about the formal anomalies. The methodology is tested in Tortosa's Gothic Cathedral's vaults, where the geometrical differences between vaults, a priori equal, are identified and related with the partially known construction phases. The procedure can be easily used on any other vaulted construction of any kind, but is especially useful to deal with the complex geometry of Gothic masonry vaults.
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
Catenary arches and vaults were used in Spain during two historical periods. First, the theoretical concept was used in the eighteenth century by military engineers for the construction of gunpowder magazines. Subsequently, Catalan modernist architects, such as Antoni Gaudí i Cornet (1852-1926) and Cèsar Martinell i Brunet (1888-1973) used this shape throughout their buildings. The paper assesses the geometric approximations to the catenary made by eighteenth-century military engineers and twentieth-century architects in Spain. The investigation is based on two documentary sources: the designs for gunpowder magazines found in the Colección de Mapas, Planos y Dibujos del Archivo General de Simancas, and the design by Cèsar Martinell i Brunet for the Cooperative wine cellar in Pinell de Brai (1918), preserved in the Arxiu Històric del ColÁlegi d'Arquitectes de Catalunya. The assessment confirms the use of the concept of the chain during these two historical periods.
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