ABSTRACT
That the building committee of the new cathedral of Milan should have asked whether its construction ought to rise according to the square or the triangle shows that designing ad quadratum was also an established method of design. The evidence for its use in architectural planning and constructional design is conclusive, yet the motives for choosing it in the first place are rarely, if ever, sought and the view is still sometimes perpetuated that it was a function of purely practical procedures on the part of medieval masons that had no other meaning. This chapter therefore will summarize the medieval evidence for the architectural use of the square and will review the mathematical and metaphysical properties attaching to it in the Middle Ages in an attempt to suggest how it could have been understood as a signifier in medieval architecture and art.1
