  The aim of this paper is to show that Plato's theory of knowledge of Forms
(intelligible Beings, Ideas) in the Sophistes, obtained by Division and
Collection, is a close philosophic analogue of the geometric theory of periodic
anthyphairesis, an ancient theory of incommensurability (developed by the
Pythagoreans, Theodorus and Theaetetus) having its modern counterpart in the
theory of continued fractions. Division corresponds to infinite anthyphairetic
division, Collection to the Logos Criterion, resulting in periodicity and a
self-similar One, precisely the One of a Platonic Form.
