Phenomenology of diagrams in Book II of the Elements

Abstract

In this paper, we provide an interpretation of Book II of the Elements from the perspective of figures which are represented and not represented on the diagrams. We show that Euclid's reliance on figures not represented on the diagram is a proof technique which enables to turn his diagrams II.11--14 into ideograms of a kind. We also discuss interpretations of Book II developed by J. Baldwin and A. Mueller, L. Corry, D. Fowler, R. Hartshorne, I. Mueller, K. Saito, and the so-called geometric algebraic interpretation in B. van der Waerden's version.