Scholars have long recognized that “practical geometry,” the shapes and proportional relationships used to regulate construction, played a key role in medieval architectural design. Within this rich discourse, an emphasis on Gothic texts and buildings has produced a general image that master masons used totalizing forms to control the relations of parts to whole (such as ad triangulum and ad quadratum schemes). But as James S. Ackerman noted more than seventy years ago, many medieval buildings do not conform to this idealized method. A detailed analysis of the Romanesque Baptistery of San Giovanni in Ascoli Piceno, Italy (an adaptation of an Early Christian baptistery) illustrates an alternative mode of practical geometry, applied not as strict, regulating forms but as patterns of action governed by consistent geometric relationships with the variables of the site. This approach proved singularly capable of “regularizing the irregular” during a period marked by the adaptive reuse of ancient buildings.

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