From Gothic to Renaissance Stereotomy: The Design Methods of Philibert de l’Orme and Alonso de Vandelvira

Abstract

From Gothic to Renaissance Stereotomy: The Design Methods of Philibert de I’Orme and Alonso de Vandelvira SERGIO LUIS SANABRIA Stereotomy is the art of cutting solids precisely so their parts fit together tightly. Although stereotomic problems arise in all masonry or wood construction in which a whole must be made of various parts, calculations are needed only for precise compound-angle or curved cuts. Cutting simple rectangular blocks demands no special knowl­ edge, and even complex cuts often can be determined empirically by approximation and fitting, in the way traditional carpenters or ancient Greek and Inca masons adjusted joints by sanding down or trimming points of contact until matching surfaces were obtained.1 Simple arches introduce a trivial complication: voussoirs require adding adjustable angle protractors, or bevels, to masons’ tool kits. Even the sloping barrel vaults of the Hellenistic temple of Apollo at Didyma could have been constructed without resort to geometric the­ ory. Complex curves based on conic sections appear in structures only after the Roman development of intersecting groin vaults. Treatises such as the Conics by Apollonius of Perga or its lost predecessor, the Four Books on Conics by Euclid, could have provided a conceptual background for this architectural innovation, although in fact they probably were superfluous. Roman builders avoided stereotomic com­ putations of vault groins by the use of mass concrete and brick that Dr. Sanabria teaches in the Department of Architecture at Miami University. He began his work on early stereotomy as part of his Princeton University dissertation under the direction of David Coffin, Robert Mark, and Michael Mahoney. His research interests include Gothic and Renaissance architecture in France and Spain, with a strong technological bent often inspired by the work of Carl Conclit. Since 1984 he has been engaged in a survey of the Cathedral of Metz to isolate its design campaigns between ca. 1215 and 1350, and he is currently writing a book on the architectural theory of Rodrigo (iil de Hontanon. 'For discussions of stonejoints in Greek temples, see Roland Martin, Manuel({'architecture grecque (Paris, 1965); and J. J. Coulton, Ancient Greek Architects at Work (Ithaca, N.Y.; 1977), pp. 46—48. For Inca work, see Jean-Pierre Protzen, “Inca Quarrying and Stonecutting ,” Journal of the Society oj Architectural Historians 44 (May 1985): 161—82.© 1989 by the Society for the History of Technology. All rights reserved. 0040- 165X/89/3002-0007$01.00 266 From, Gothic to Renaissance Stereotomy 267 were shaped with temporary wooden formwork. Using thick mortar joints, one can rely on formwork definition even in cut stone vaults. Carolingian and Early Romanesque stone vaults are examples, as are the infill webs of most Gothic rib vaults.2 Among the earliest buildings exhibiting stéréotomie skills is the Theater at Philippolis in Syria, with groin vaults executed in cut stone. Seven centuries later, in a.d. 965, more complex stéréotomie problems arise in stellar rib vaults built in the expansion of the Friday Mosque of Cordoba under al-Hakim IE The vaults, with up to three arches intersecting at compound angles, exhibit precisely cut bosses shaped as irregular polyhedra. These crisscrossing rib vaults spread beyond Spain in the 12th century to churches in the French Pyrenees and as far east as Armenia. Still later is the famous 12th-century vis St. Gilles, a hélicoïdal barrel vault carrying a spiral staircase on the north tran­ sept of the Romanesque abbey church of St. Gilles du Gard in Pro­ vence. The helicoidally warped surfaces of individual voussoirs ht smoothly against each other, creating a curved surface of extraordi­ nary elegance. Stereotomy and Constructive Geometry Flow were these opera mirabilia designed? Euclid and Apollonius of Perga had been available in Arabic translations since the 10th century, but, given the widespread illiteracy among Islamic and Christian ma­ sons, the necessary geometric training for exact stereotomic compu­ tations seems unlikely. Although evidence for the geometric training of Islamic craftsmen in Spain is very late, it suggests an adherence to rules learned by rote in the shops rather than an understanding of the mathematical structure of problems.3 Thus, even if a mathema­ tician were hired to solve the stereotomic...