Projection and the Ubiquitous Virtue of Geometry in the Renaissance

Abstract

The role of mathematics, of geometry in particular, has been a traditional focus of interest for historians of Renaissance and early-modern science. The acceptance of the explanatory power of geometry in natural philosophy, and its accommodation to both an experimental methodology and a mechanistic narrative of causality, are issues that continue to be addressed, even though greater emphasis is placed nowadays on historicist accounts of practice than on recovering grand conceptual congruences between philosophical traditions. A shift of attention on to practice will bring to notice one of the most curiously neglected aspects of the mathematics of fifteenth- and sixteenth-century Europe — a period where it would be natural to look for the roots of the application of geometry to natural philosophy in the seventeenth century. Before it laid claim to a central role in natural philosophy, geometry had been conspicuous in the reform of a range of practical arts and sciences, from painting and architecture to surveying, fortification and navigation, and this record became part of the authority for extending the proven virtue of geometry to accounting for the natural world.