Origin of the term “phantasia” for infinite divisibility in Greek mathematical commentaries

Determine whether the usage of the term “phantasia” to denote the infinite divisibility of magnitudes in the Anonymon Scholion X.2 to Euclid’s Elements and in Proclus’s Commentary to Euclid originates from Plato’s Theaetetus 147d7–8 (“since the powers appeared infinite in multitude”) and was introduced by Proclus. Establish the historical-linguistic evidence confirming or refuting this proposed provenance and coinage.

Background

In discussing the Anonymon Scholion X.2 to Euclid’s Elements, the authors note that the scholion employs the term “phantasia” (imagination) in connection with the infinitely divisible nature of magnitudes. They connect this to Proclus’s extended remarks on imagination and the infinite in his Commentary to Euclid.

They explicitly propose a conjecture about the provenance of this usage, suggesting it derives from Plato’s Theaetetus 147d7–8, where the powers are said to appear infinite in multitude, and further suggest that Proclus likely coined this specific application of the term. Clarifying the historical origin would strengthen the philological and historiographical basis of their reconstruction.