Geometrical Bodies as Material Forms: Luca Pacioli's 'Summa', 'Divina Proportione', 'Euclid's Elements', and the Architecture of the Late Fifteenth-Early Sixteenth Century

This thesis considers how and why geometrical bodies were regarded as exemplary forms in Luca Pacioli's works and by which means these were applied to architecture, and compares Pacioli's position with those of other architectural theorists. To accomplish this, it relies on an understanding of human visuality coherent with the latest research in the psychology and philosophy of perception.

Pacioli was a lecturer in mathematics, was exceptionally well-placed in some of the most learned courtly environments and was very receptive to philosophical and mathematical trends. He was also very able when these had to be summarised or developed in his works. Pacioli's works stand at the intersection of the theoretical and practical knowledge of the late fifteenth and early sixteenth centuries.

These are therefore extraordinary documents with which to trace the interrelation of philosophical, mathematical, and architectural arguments and consider the work of the practitioners with whom Pacioli interacted. Lastly, this thesis examines Pacioli's arguments on geometrical bodies and their application to the architecture of Donato Bramante, in their philosophical and theoretical contexts. Ultimately, the contextual analysis of Pacioli's arguments and Bramante's innovative design process clarifies not only their inherent correlations, but also their relevance to present-day approaches to the formal, visual, and spatial properties of architecture.