Phenomenology of diagrams in Book II of the Elements

TL;DR

This paper interprets Book II of Euclid's Elements, highlighting the role of unrepresented figures as proof techniques and ideograms, and discusses various scholarly interpretations of the text.

Contribution

It offers a novel perspective on Euclid's use of diagrams and unrepresented figures, connecting historical interpretations with modern understanding.

Findings

Euclid's reliance on unrepresented figures functions as a proof technique.

Unrepresented figures serve as ideograms in Euclidean geometry.

The paper compares multiple scholarly interpretations of Book II.

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.