“That small and unsensible shape”: Visual Representations of the Euclidean Point in Sixteenth-Century Print

Abstract

This paper probes the foundations and limits of visual representation in the sciences through a close reading of the diagrams that accompanied definitions of the geometric point in the first century of printed editions of Euclid’s Elements. I begin with the modal form for such diagrams of Euclid’s “small and unsensible shape,” showing how it incorporates a broad spectrum of conventions and practices related to the point’s philosophical and practical roles in the surrounding Euclidean geometry. I then explore the form’s several variations in order to consider the role of “mere representation” in geometric exegesis, and conclude by characterizing the curious relationship between things and their images and that relationship’s implications for understanding scientific knowledge and practice.