Note 767 — Chapter VII · THE PYTHAGOREANS

Heiberg’s Euclid, vol. v. p. 654, 1, Ἐν τούτῳ τῷ βιβλίῳ, τουτέστι τῷ ιγ’, γράφεται τὰ λεγόμενα Πλάτωνος ε̄ σχήματα, ἃ αὐτοῦ μὲν οὐκ ἔστιν, τρία δὲ τῶν προειρημένων ε̄ σχημάτων τῶν Πυθαγορείων ἐστίν, ὅ τε κύβος καὶ ἡ πυραμὶς καὶ τὸ δωδεκάεδρον, Θεαιτήτου δὲ τό τε ὀκτάεδρον καὶ τὸ εἰκοσάεδρον. It is no objection to this that, as Newbold points out (Arch. xix. p. 204), the inscription of the dodecahedron is more difficult than that of the octahedron and icosahedron. The Pythagoreans were not confined to strict Euclidean methods. It may further be noted that Tannery comes to a similar conclusion with regard to the musical scale described in the fragment of Philolaos. He says: “Il n’y a jamais eu, pour la division du tétracorde, une tradition pythagoricienne; on ne peut pas avec sûreté remonter plus haut que Platon ou qu’Archytas” (Rev. de Philologie, 1904, p. 244).