  In the present work it is shown, by an examination of the Platonic dialogues
Theaetetus, Sophistes, Politicus, and Philebus, that (a) a Platonic Idea is the
philosophic analogue of a pair of lines incommensurable in length only, (b) the
Division and Collection, the method by which humans obtain knowledge of a
Platonic Idea, is the philosophic analogue of the palindromically periodic
anthyphairesis of this pair, and (c) a Platonic Idea is One in the sense of the
self-similarity induced by periodic anthyphairesis.
  A byproduct of the above analysis is that (d) Theaetetus had obtained a proof
of the Proposition: The anthyphairesis of a dyad of lines incommensurable in
length only is palindromically periodic. It is further verified that the
concepts and tools contained in the Theaetetean Book X of the Elements suffice
for the proof of the Proposition.
