But there was also, not far from these times, another philosophy which Pythagoras originated (who some say was a native of Samos), which they have denominated Italian, because that Pythagoras, flying from Polycrates the king of Samos, took up his residence in a city of Italy, and there passed the entire of his remaining years. And they who received in succession his doctrine, did not much differ from the same opinion. And this person, instituting an investigation concerning natural phenomena, [45] combined together astronomy, and geometry, and music. [46] And so he proclaimed that the Deity is a monad; and carefully acquainting himself with the nature of number, he affirmed that the world sings, and that its system corresponds with harmony, and he first resolved the motion of the seven stars into rhythm and melody. And being astonished at the management of the entire fabric, he required that at first his disciples should keep silence, as if persons coming into the world initiated in (the secrets of) the universe; next, when it seemed that they were sufficiently conversant with his mode of teaching his doctrine, and could forcibly philosophize concerning the stars and nature, then, considering them pure, he enjoins them to speak. This man distributed his pupils in two orders, and called the one esoteric, but the other exoteric. And to the former he confided more advanced doctrines, and to the latter a more moderate amount of instruction.

And he also touched on magic -- as they say -- and himself [47] discovered an art of physiogony, [48] laying down as a basis certain numbers and measures, saying that they comprised the principle of arithmetical philosophy by composition after this manner. The first number became an originating principle, which is one, indefinable, incomprehensible, having in itself all numbers that, according to plurality, can go on ad infinitum. But the primary monad became a principle of numbers, according to substance, [49] -- which is a male monad, begetting after the manner of a parent all the rest of the numbers. Secondly, the duad is a female number, and the same also is by arithmeticians termed even. Thirdly, the triad is a male number. This also has been classified by arithmeticians under the denomination uneven. And in addition to all these is the tetrad, a female number; and the same also is called even, because it is female. Therefore all the numbers that have been derived from the genus are four; but number is the indefinite genus, from which was constituted, according to them, the perfect [50] number, viz., the decade. For one, two, three, four, become ten, if its proper denomination be preserved essentially for each of the numbers. Pythagoras affirmed this to be a sacred quaternion, source of everlasting nature, [51] having, as it were, roots in itself; and that from this number all the numbers receive their originating principle. For eleven, and twelve, and the rest, partake of the origin of existence [52] from ten. Of this decade, the perfect number, there are termed four divisions, -- namely, number, monad, [53] 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 [54] 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, [55] 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, [56] and Aristoxenus [57] the musician, assert that Pythagoras came to Zaratas [58] the Chaldean, and that he explained to him that there are two original causes of things, father and mother, and that father is light, but mother darkness; and that of the light the parts are hot, dry, not heavy, light, swift; but of darkness, cold, moist, weighty, slow; and that out of all these, from female and male, the world consists. But the world, he says, is a musical harmony; [59] wherefore, also, that the sun performs a circuit in accordance with harmony. And as regards the things that are produced from earth and the cosmical system, they maintain that Zaratas [60] makes the following statements: that there are two demons, the one celestial and the other terrestrial; and that the terrestrial sends up a production from earth, and that this is water; and that the celestial is a fire, partaking of the nature of air, hot and cold. [61] And he therefore affirms that none of these destroys or sullies the soul, for these constitute the substance of all things. And he is reported to have ordered his followers not to eat beans, because that Zaratas said that, at the origin and concretion of all things, when the earth was still undergoing its process of solidification, [62] and that of putrefaction had set in, the bean was produced. [63] And of this he mentions the following indication, that if any one, after having chewed a bean without the husk, places it opposite the sun for a certain period, -- for this immediately will aid in the result, -- it yields the smell of human seed. And he mentions also another clearer instance to be this: if, when the bean is blossoming, we take the bean and its flower, and deposit them in a jar, smear this over, and bury it in the ground, and after a few days uncover it, we shall see it wearing the appearance, first of a woman's pudendum, and after this, when closely examined, of the head of a child growing in along with it. This person, being burned along with his disciples in Croton, a town of Italy, perished. And this was a habit with him, whenever one repaired to him with a view of becoming his follower, (the candidate disciple was compelled) to sell his possessions, and lodge the money sealed with Pythagoras, and he continued in silence to undergo instruction, sometimes for three, but sometimes for five years. And again, on being released, he was permitted to associate with the rest, and remained as a disciple, and took his meals along with them; if otherwise, however, he received back his property, and was rejected. These persons, then, were styled Esoteric Pythagoreans, whereas the rest, Pythagoristæ.

Among his followers, however, who escaped the conflagration were Lysis and Archippus, and the servant of Pythagoras, Zamolxis, [64] who also is said to have taught the Celtic Druids to cultivate the philosophy of Pythagoras. And they assert that Pythagoras learned from the Egyptians his system of numbers and measures; and being struck by the plausible, fanciful, and not easily revealed wisdom of the priests, he himself likewise, in imitation of them, enjoined silence, and made his disciples lead a solitary life in underground chapels. [65]

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Footnotes:

[45] Or, "nature."

[46] "And arithmetic" (added by Roeper).

[47] Or, "and he first."

[48] Or, "physiognomy."

[49] Or, "in conformity with his hypothesis."

[50] Or, "the third."

[51] Or, "an everlasting nature;" or, "having the roots of an everlasting nature in itself," the words "as it were" being omitted in some mss.

[52] Or, "production."

[53] 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.

[54] Kobisthe in text must be rendered "multiplied." The formulary is self-evident: (a^2)^2 = a^4, (a^2)^3 = a^6, (a^3)^3 = a^9.

[55] 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.)

[56] 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.

[57] 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 sensation being the result of nerval vibrations. Cicero says of Aristoxenus, "that he was so charmed with his own harmonies, that he sought to transfer them into investigations concerning our corporeal and spiritual nature."

[58] Zaratas is another form of the name Zoroaster.

[59] Or, "is a nature according to musical harmony" (preceding note); or, "The cosmical system is nature and a musical harmony."

[60] Zaratas, or Zoroaster, is employed as a sort of generic denomination for philosopher by the Orientals, who, whatever portions of Asia they inhabit, mostly ascribe their speculative systems to a Zoroaster. No less than six individuals bearing this name are spoken of. Arnobius (Contr. Gentes., i. 52) mentions four--(1) a Chaldean, (2) Bactrian, (3) Pamphylian, (4) Armenian. Pliny mentions a fifth as a native of Proconnesus ( Nat. Hist.., xxx. 1), while Apuleius (Florida, ii. 15) a sixth Zoroaster, a native of Babylon, and contemporary with Pythagoras, the one evidently alluded to by Hippolytus. (See translator's Treatise on Metaphysics, chap. ii.)

[61] Or, "that it was hot and cold," or "hot of moist."

[62] Or it might be rendered, "a process of arrangement." The Abbe Cruice (in his edition of Hippolytus, Paris, 1860) suggests a different reading, which would make the words translate thus, "when the earth was an undigested and solid mass."

[63] [See book vi. cap. xxii., infra, and note. But Clement gives another explanation. See vol. ii. p. 385, this series.]

[64] Or, "Zametus."

[65] Or, "leading them down into cells, made them," etc.; or, "made his disciples observe silence," etc.