The Geometry of San Xavier del Bac and la Purisima Concepciop De Nuestra Senora De Caborca
Schuetz-Miller, Mardith, Journal of the Southwest
Early Renaissance architects retained the tradition from master builders of the Middle Ages of using the square, equilateral triangle, and eight-pointed star in designing monumental edifices. Indeed, these basic geometric forms had been used for that purpose since the Neolithic period, when geometry was sacred and was the carefully guarded secret of priest or king builders. Geometry, numbers, and the concept of time evolved out of human observations of celestial movements--subjects that were sacred in themselves because they reflected the heavenly abode of the gods. The geometric figures of circle, square, star, and triangle, like numbers, were replete with esoteric meanings. As examples, the eight-pointed star and triangle were originally associated with the Great Goddesses of antiquity. The eight-pointed star and number eight retained their mystic qualities through time. The star remained arguably the most important figure used in designing sacred structures. The octagon, popular with Byzantine builders of early Christian structures and introduced by them to the West, bridged the square of the earth with the dome of heaven and simultaneously reflected the eight winds or eight directions. The equilateral triangle came to be symbolic of the Christian Trinity. Geometric forms and numbers associated with mysticism were integrated into the religious beliefs of all high civilizations of the ancient world. In the West it permeated Pythagorean and Platonic teachings, which were embraced by fathers of the Medieval Christian church in their quest for order and harmony in the natural world.
The Roman builder Vitruvius recorded some of the applications of geometry to building design that were known to masters of old. His Ten Books on Architecture, which emphasized the geometric basis of commensurable ratios, continued in circulation throughout the Middle Ages in various manuscript forms. An interest in geometric forms inherent in nature during the thirteenth century is evident in the Sketchbooks of Villard de Honnecourt, which include additional drawings by a builder known only as "Magister 2." In a late-fifteenth-century treatise, Matthias Roritzer demonstrated the doubling of the square. Renaissance concern for harmonic proportions led to the publication of books on architecture by a few German masters and such well-known Italian architects as Alberti, Serlio, Vignola, and Palladio--all of whom built upon the Vitruvian base. Transmission of the time-tested secrets of geometric design thus continued for some six thousand years. The esoteric knowledge, once known only to kings and priests of theocratic states, had come to be entrusted to civilian master builders, and thus the guilds pertaining to the building trades, with strong links to the church, came to be the keepers of the arcane wisdom. Guilds reached the apex of their power along with the independence of towns in the Medieval period, but by the eighteenth century fell into abusive practices in their attempt to hang onto their monopolies in a world changed forever by the formation of modern nations and the Industrial Revolution. France abolished its guilds in 1791, England followed suit in 1813--although in the case of the English building trades, their monopoly had been broken a century earlier. The Spanish monarchy, likewise, had undermined the power of the guilds long before they were officially dissolved, also in 1813.
But tradition is not easily discarded despite official edicts. Guilds of masons and carpenters were in place in San Antonio, Texas, on New Spain's northern frontier as late as 1809, operating without viceregal interference, while Mexico City had circumvented a closed shop by establishing the Academy of San Carlos in 1785, where architects matriculated who lacked any experience in actual building. Thus, on the northern borderlands we find master masons and stonecutters from the interior provinces of Mexico contracted to design and construct the permanent churches of the border states late in the colonial period. …