New Theories for New Instruments: Fabrizio Mordente’s Proportional Compass and the Genesis of Giordano Bruno’s Atomist Geometry

The aim of this paper is to shed light on an understudied aspect of Giordano Bruno's intellectual biography, namely, his career as a mathematical practitioner. Early interpreters, especially, have criticized Bruno's mathematics for being “outdated” or too “concrete”. However, thanks to developments in the study of early modern mathematics and the rediscovery of Bruno's first mathematical writings (four dialogues on Fabrizio's Mordente proportional compass), we are in a position to better understand Bruno's mathematics. In particular, this paper aims to reopen the question of whether Bruno anticipated the concept of infinitesimal quantity. It does so by providing an analysis of the dialogues on Mordente's compass and of the historical circumstances under which those dialogues were written. Mordente's compass was almost unknown until the late 1800s, as its existence was overshadowed by that of another proportional compass, invented by a better-known Italian scientist: Galileo Galilei. However, Mordente's compass did not go completely unnoticed by his contemporaries, catching the eye of technicians and mathematical practitioners, but also of speculative thinkers like Bruno. Puzzled by the novelty of Mordente’s invention, Bruno offered to write an exposition of the compass in the form of dialogues. In these dialogues, in an attempt to provide a theoretical explanation for the use of the compass, Bruno presented the first version of his atomist geometry based on the concept of the "minimum". This minimum was in essence an infinitely small quantity. As such, I argue that it can be regarded as a forerunner of the infinitesimals.