From Chapter VII., The Pythagoreans
147. The Numbers and the Elements
We must not take it for granted, however, that the Pythagorean construction of the elements was exactly the same as that we find in Plato's Timaeus. As we have seen, there is good reason for believing they only knew three of the regular solids, the cube, the pyramid (tetrahedron), and the dodecahedron.70 Now Plato makes Timaios start from fire and earth,71 and in the construction of the elements he proceeds in such a way that the octahedron and the icosahedron can easily be transformed into pyramids, while the cube and the dodecahedron cannot. From this it follows that, while air and water pass readily into fire, earth cannot do so,72 and the dodecahedron is reserved for another purpose, which we shall consider presently. This would exactly suit the Pythagorean system; for it would leave room for a dualism of the kind outlined in the Second Part of the poem of Parmenides. We know that Hippasos made Fire the first principle, and we see from the Timaeus how it would be possible to represent air and water as forms of fire. The other element is, however, earth, not air, as we have seen reason to believe that it was in early Pythagoreanism. That would be a natural result of the discovery of atmospheric air by Empedokles and of his general theory of the elements. It would also explain the puzzling fact, which we had to leave unexplained above, that Aristotle identifies the two "forms" spoken of by Parmenides with Fire and Earth.73
68. All this has been put in its true light by the publication of the extract from Menon's Ἰατρικά on which see p. 278, n. 4.
69. In Aet. ii. 6, 5 (R. P. 80) the theory is ascribed to Pythagoras, which is an anachronism, as the mention of "elements" shows it must be later than Empedokles. In his extract from the same source, Achilles says οἱ Πυθαγόρειοι which doubtless represents Theophrastos better.
70. See above p. 283.
71. Plato, Tim. 31 b 5.
72. Plato, Tim. 54 c 4. It is to be observed that in Tim. 48 b 5 Plato says of the construction of the elements οὐδείς πω γένεσιν αὐτῶν μεμήνυκεν, which implies that there is some novelty in the theory as Timaios states it. If we read the passage in the light of what has been said in § 141, we shall be inclined to believe that Plato is making Timaios work out the Pythagorean doctrine on the lines of the discovery of Theaitetos.
73. See above, Chap. IV. p. 186.
Created for Peithô's Web from Early Greek Philosophy by John Burnet, 3rd edition (1920). London: A & C Black Ltd. Burnet's footnotes have been converted to chapter endnotes. Greek unicode text entered with Peithô's Younicoder.
Web design by Larry Clark and RSBoyes (Agathon). Peithô's Web gratefully acknowledges the assistance of Anthony Beavers in the creation of this web edition of Burnet. Please send comments to: