—namely, number, monad,[1] square, [and] cube. And the connections and blendings of these are performed, according to nature, for the generation of growth completing the productive number. For when the square itself is multiplied[2] into itself, a biquadratic is the result. But when the square is multiplied into the cube, the result is the product of a square and cube; and when the cube is multiplied into the cube, the product of two cubes is the result. So that all the numbers from which the production of existing [numbers] arises, are seven,—namely, number, monad, square, cube, biquadratic, quadratic-cube, cubo-cube.
This philosopher likewise said that the soul is immortal, and that it subsists in successive bodies. Wherefore he asserted that before the Trojan era he was Æthalides,[3] and during the Trojan epoch Euphorbus, and subsequent to this Hermotimus of Samos, and after him Pyrrhus of Delos; fifth, Pythagoras. And Diodorus the Eretrian,[4] and Aristoxenus[5] the musician, assert that Pythagoras came to
- ↑ It should be probably, "monad, number." The monad was with Pythagoras, and in imitation of him with Leibnitz, the highest generalization of number, and a conception in abstraction, commensurate with what we call essence, whether of matter or spirit.
- ↑ κοβισθῇ in text must be rendered "multiplied." The formulary is self-evident: .
- ↑ Or Thallis. Æthalides, a son of Hermes, was herald of the Argonauts, and said never to have forgotten anything. In this way his soul remembered its successive migrations into the bodies of Euphorbus, Hermotimus, Pyrrhus, and Pythagoras. (See Diogenes' Lives, book viii. chap. i. sec. 4.)
- ↑ No name occurs more frequently in the annals of Greek literature than that of Diodorus. One, however, with the title "of Eretria," as far as the translator knows, is mentioned only by Hippolytus; so that this is likely another Diodorus to be added to the long list already existing. It may be that Diodorus Eretriensis is the same as Diodorus Crotoniates, a Pythagorean philosopher. See Fabricius' Biblioth. Græc. lib. ii. cap. iii., lib. iii. cap. xxxi.; also Meursius' Annotations, p. 20, on Chalcidius' Commentary on Plato's Timæus. The article in Smith's Dictionary is a transcript of these.
- ↑ Aristoxenus is mentioned by Cicero in his Tusculan Questions, book i. chap, xviii., as having broached a theory in psychology, which may have suggested, in modern times, to David Hartley his hypothesis of
