Theodorus’ proofs of incommensurabilities with Gnomons

An ‘infinite decreasing sequence of Gnomons’ is characteristic, according to Proclus, of incommensurability, hence David Fowler's idea to reconstruct Theodorus’ proofs of incommensurabilities, reported in the Theaetetus147d, employing Gnomons, is attractive and solidly based. The ‘preservation of the shape of the Gnomons’ is a form of the Pythagorean principle of the Limited according to Aristotle. In the present paper we propose a reconstruction that employs Gnomons but is free of the drawbacks present in Fowler's reconstruction.