Roger Bacon's Mathematics: Demonstrative System and Metaphysics in the Communia Mathematica

In Communia Mathematica Roger Bacon (ca. 1214-1294) sketches why and how mathematics can be useful, or useless, for all other sciences, including metaphysics and theology. Bacon's work provides a synthesis of mathematical notions, essentially selected from the Elements by Euclid. In a large part of Communia Mathematica, the Doctor mirabilis especially engages with ratios and proportions, and he considers that their properties are able to shed light on peculiar aspects of some theological and philosophical problems, such as Trinity. In his account, several guidelines are given to outline how a system of science works, what its components are and how many demonstrative styles there are. Bacon's mathematics has a didactic finality, it is a means to acquiring reasoning's modes and it allows to reveal the core of things. Mathematics require both speculation and practice, as it transpires when the most abstract geometrical notions keep working when applied to practice.