Mathematics in the work of Spinoza and Guarini

Abstract

During the seventeenth century mathematics and the exact sciences brought about a scientific revolution, and seemed to be involved in all novel social developments of the time. To give just a few examples, Newton (1643-1727) used mathematical principles to explain the philosophy of nature in his Principia, and, prior to that, Descartes (1569-1650) used mathematics as a model for his metaphysics, his main concern for many years. His greatest legacy, for the purposes and framing of this paper, has to do with moving classical geometry within the reach of algebra, putting into connection Euclid's and Vitruvius’s theories. This has great relevance within the field of architecture, translating these theories to the building experience of that period. Baroque architecture indeed shares with mathematics a spatial structure which combines the arts and the sciences. Space is controlled by the possible variations of mathematical laws — which is the cause of the way in which architects struggle to work within pre-established rules.The aim of this paper, intended as research from a history of architectural points of view, is to find relations between the idea of mathematics used by Spinoza (Ethics) and Guarini (Placita philosophica; Architettura civile) in their metaphysics, and the outcomes they had in architecture. In addition, if it is difficult to establish whether Spinoza had any influence on Guarini — their most relevant texts were published posthumously — the role of mathematics in the work of these two figures, whose similarities and differences are worth enumerating, is particularly interesting when related to the architectural period of Baroque, a period when the use of mathematics in architecture might be said to have reached a peak.