Distributivity-like Results in Euclid’s Elements

Abstract

The present chapter presents a preliminary overview of some propositions of Books II, V, and VII of Euclid’s Elements that, retrospectively seen, embody results that we can associate nowadays with a more general idea of distributivity. It focuses on several results and arguments that are handled differently by Euclid in three clearly separate contexts: geometric magnitudes, arithmetic and numbers, and proportions. It also discusses Euclidean propositions where “visible” constructions implicitly use distributive-like properties.