are one, if the word is is used in one sense only (Parmenides), by affirming the reality of what is not; to the second, that based on dichotomy (Zeno), by introducing indivisible magnitudes." Finally, it is only by regarding the matter in this way that we can attach any meaning to another statement of Aristotle's that Leukippos and Demokritos, as well as the Pythagoreans, virtually make all things out of numbers.[1] Leukippos, in fact, gave the Pythagorean monads the character of the Parmenidean One.
174.Atoms. We must observe that the atom is not mathematically indivisible, for it has magnitude; it is, however, physically indivisible, because, like the One of Parmenides, it contains no empty space.[2] Each atom has extension, and all atoms are exactly alike in substance.[3] Therefore all differences in things must be accounted for either by the shape of the atoms or by their arrangement. It seems probable that the three ways in which differences arise, namely, shape, position, and arrangement, were already distinguished by Leukippos; for Aristotle mentions his name in connexion with them.[4] This explains, too, why the atoms are called "forms" or "figures," a way of speaking which is clearly of Pythagorean origin.[5] That they are also called
- ↑ Arist. De caelo, Γ, 4. 303 a 8, τρόπον γάρ τινα καὶ οὗτοι (Λεύκιππος καὶ Δημόκριτος) πάντα τὰ ὄντα ποιοῦσιν ἀριθμοὺς καὶ ἐξ ἀριθμῶν. This also serves to explain the statement of Herakleides attributing the theory of corporeal ὄγκοι to the Pythagorean Ekphantos of Syracuse (above, p. 291, n. 3).
- ↑ The Epicureans misunderstood this point, or misrepresented it in order to magnify their own originality (see Zeller, p. 857, n. 3).
- ↑ Arist. De caelo, A, 7. 275 b 32, τὴν δὲ φύσιν εἶναί φασιν αὐτῶν μίαν. Here φύσις can only have one meaning. Cf. Phys. Γ, 4. 203 a 34, αὐτῷ (Δημοκρίτῳ) τὸ κοινὸν σῶμα πάντων ἐστὶν ἀρχή.
- ↑ Arist. Met. A, 4. 985 b 13 (R. P. 192); cf. De gen. corr. A, 2. 315 b 6. As Diels suggests, the illustration from letters is probably due to Demokritos. It shows, in any case, how the word στοιχεῖον came to be used for "element." We must read, with Wilamowitz, τὸ δὲ Ζ τοῦ Η θέσει for τὸ δὲ Ζ τοῦ Ν θέσει, the older form of the letter Z being just an H laid upon its side (Diels, Elementum, p. 13, n. 1).
- ↑ Demokritos wrote a work, Περὶ ἰδεῶν (Sext. Math. vii. 137 ; R. P. 204), which Diels identifies with the Περὶ τῶν διαφερόντων ῥυσμῶν of Thrasylos, Tetr. v. 3. Theophrastos refers to Demokritos, ἐν τοῖς περὶ τῶν εἰδῶν (De sensibus, § 51). Plut. Adv. Col. 1111 a, εἶναι δὲ πάντα τὰς
