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Throughout history, diagrammatic drawing formed a  modus operandi  for generating architectural typologies, creating spatial hierarchies, codifying ratio and proportion while defining the shape grammar of the edifice. Despite the prominence of the diagram in architectural design, no account of designing irregular sites during the Renaissance exists, nor how diagrams partition space. This paper’s computer-aided graphical analysis elucidates how to design irregular sites by reading principles of partitioning in the treatises of Serlio and Palladio. Through the numeric lexicons of Serlio, Palladio and Bertotti Scamozzi, this paper uncovers the ways the transformative power of the diagram codifies irregular typologies while ordering its spatial hierarchies. The cases of Serlio’s and Palladio’s geometrical reckoning illuminate a commonplace working method for partitioning Renaissance palazzi where the heuristic diagram visually uncovers the architect’s idea by combining context, site, and function that result in architectural inventions.

Partitioning Sites for Invention in Serlio’s and Palladio’s Palazzi