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The existing fragments of an architectural booklet by the 16th-century Spanish architect Rodrigo Gil de Hontañón reveal an ingenious attempt to systematize the design process by creating a sequence of formulaic procedures to be followed in ecclesiastical projects. The formulae are addressed to two more or less separate issues. The first is to synthesize Gothic and Classic proportioning methods, and demonstrate their fundamental identity. The second is to establish an independent "science" of structural design. Aside from the more theoretical writings of Leonardo da Vinci, the work of Rodrigo Gil is the principal evidence extant for the development of structural thinking among 16th-century master masons. Seven formulae discussed here are concerned with the correct depth of a buttress to support an arch or a rib vault. The formulae do not seem to have been derived through theoretical analysis, using the medieval Scientia de Ponderibus. Rather they are the result of new experimentation and traditional Gothic geometric thinking applied to classical arches, and of new arithmetic procedures applied to Gothic rib vaults.

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