Semantic Annotation of Ancient Greek Mathematical Texts

In his Commentary on Book I of Euclid's Elements, Proclus Lycius, a famous Neoplatonic philosopher of the fifth century CE, proposed a scheme for analyzing complete mathematical propositions into six parts: proposition, enunciation, setting out, determination, construction, proof and conclusion. Leaving content aside, most of these parts can be identified based on specific formulaic expressions. Still, neither all parts are always identifiable by such expressions, nor do they always appear in a strictly sequential order with no intermingling with each other. This paper focuses on developing a tool which will allow scholars to semantically annotate ancient Greek mathematical texts according to Proclus' scheme. To this end, we apply machine learning algorithms to the first seven books of Euclid's Elements.