Chapter II.—Pythagoras; His Cosmogony; Rules of His Sect; Discoverer of Physiognomy; His Philosophy of Numbers; His System of the Transmigration of Souls; Zaratas on Demons; Why Pythagoras Forbade the Eating of Beans; The Mode of Living Adopted by His Disciples.

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,26    Or, “nature.”    The text is corrupt, but the above seems probably the meaning, and agrees with the rendering of Schneidewin and Cruice. combined together astronomy, and geometry, and music.27    “And arithmetic” (added by Roeper).    Or, “view.” 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 himself28    Or, “and he first.”    The clepsydra, an instrument for measuring duration, was, with the sun-dial, invented by the Egyptians under the Ptolemies. It was employed not only for the measurement of time, but for making astronomic calculations. Water, as the name imports, was the fluid employed, though mercury has been likewise used. The inherent defect of an instrument of this description is mentioned by Hippolytus. discovered an art of physiogony,29    Or, “physiognomy.”    Literally, “twisting, tergiversating.” 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,30    Or, “in conformity with his hypothesis.”    This seems the meaning, as deducible from a comparison of Hippolytus with the corresponding passage in Sextus Empiricus.—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 perfect31    Or, “the third.”    Omitted by Sextus. 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,32    Or, “an everlasting nature;” or, “having the roots of an everlasting nature in itself,” the words “as it were” being omitted in some mss.    The Abbe Cruice observes, in regard of some verbal difference here in the text from that of Sextus, that the ms. of The Refutation was probably executed by one who heard the extracts from other writers read to him, and frequently mistook the sound. The transcriber of the ms. was one Michael, as we learn from a marginal note at the end. 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 existence33    Or, “production.” from ten. Of this decade, the perfect number, there are termed four divisions,—namely, number, monad,34    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. 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 multiplied35    Κοβισθῂ in text must be rendered “multiplied.” The formulary is self-evident: (a2)2 = a4, (a2)3 = a6, (a3)3 = a9. 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,36    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.) 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,37    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. and Aristoxenus38    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.” the musician, assert that Pythagoras came to Zaratas39    Zaratas is another form of the name Zoroaster. 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;40    Or, “is a nature according to musical harmony” (preceding note); or, “The cosmical system is nature and a musical harmony.” 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 Zaratas41    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.) 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.42    Or, “that it was hot and cold,” or “hot of moist.” 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,43    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.” and that of putrefaction had set in, the bean was produced.44    [See book vi. cap. xxii., infra, and note. But Clement gives another explanation. See vol. ii. p. 385, this series.] 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,45    Or, “Zametus.” 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.46    Or, “leading them down into cells, made them,” etc.; or, “made his disciples observe silence,” etc.

[2] Ἔστι δὲ καὶ ἑτέρα φιλοσοφία οὐ μακρὰν τῶν αὐτῶν χρόνων, ἧς ἦρξε Πυθαγόρας, ὃν Σάμιόν τινες λέγουσιν. ἣν Ἰταλικὴν προσηγόρευσαν διὰ τὸ τὸν Πυθαγόραν φεύγοντα Πολυκράτην τὸν Σαμίων τύραννον οἰκῆσαι πόλιν τῆς Ἰταλίας κἀκεῖ τὸν βίον πληρῶσαι. οὗ τὴν αἵρεσιν οἱ διαδεξάμενοι οὐ πολὺ διήνεγκαν τοῦ αὐτοῦ φρονήματος. καὶ αὐτὸς δὲ περὶ φυσικῶν ζητήσας ἔμιξεν ἀστρονομίαν καὶ γεωμετρίαν καὶ μουσικὴν [καὶ ἀριθμητικήν]: καὶ οὕτως μονάδα μὲν εἶναι ἀπεφήνατο τὸν θεόν, ἀριθμοῦ δὲ φύσιν περιέργως καταμαθὼν μελῳδεῖν ἔφη τὸν κόσμον καὶ [καθ'] ἁρμονίαν συγκεῖσθαι, καὶ τῶν ἑπτὰ ἄστρων πρῶτος τὴν κίνησιν εἰς ῥυθμὸν καὶ μέλος [ἀν]ήγαγεν. θαυμάσας δὲ τὴν διοίκησιν τῶν ὅλων ἠξίωσε τὰ πρῶτα σιγᾶν τοὺς μαθητάς, οἱονεὶ μύστας τοῦ παντὸς εἰς τὸν κόσμον ἥκοντας: εἶτα ἐπειδὰν αὐτοῖς ἱκανῶς παιδείας τῆς τῶν λόγων δόξῃ μετεῖναι καὶ δυνατῶς περὶ ἄστρων καὶ φύσεως φιλοσοφήσωσι, καθαροὺς κρίνας τότε κελεύει φθέγγεσθαι. οὗτος τοὺς μαθητὰς διεῖλε καὶ τοὺς μὲν ἐσωτερικούς, τοὺς δὲ ἐξωτερικοὺς ἐκάλεσεν: τοῖς μὲν γὰρ τὰ τελεώτερα μαθήματα ἐπίστευε, τοῖς δὲ τὰ μετριώτερα. ἐφήψατο δὲ καὶ μαγικῆς, ὥς φασι, καὶ φυσιογνωμονικὴν αὐτὸς ἐξεῦρεν. Ἀριθμοὺς [δέ] τινας καὶ μέτρα ὑποθέμενος λέγει τὴν ἀρχὴν τῆς ἀριθμητικῆς [τὴν] φιλοσοφίαν κατὰ σύνθεσιν περιέχειν τόνδε τὸν τρόπον. ἀριθμὸς γέγονε πρῶτος ἀρχή_ὅπερ ἐστὶν ἕν, ἀόριστον, ἀκατάληπτον_, ἔχων ἐν ἑαυτῷ πάντας τοὺς ἐπ' ἄπειρον δυναμένους ἐλθεῖν ἀριθμοὺς κατὰ τὸ πλῆθος. τῶν δὲ ἀριθμῶν ἀρχὴ γέγονε καθ' ὑπόστασιν ἡ πρώτη μονάς, ἥτις ἐστὶ μονὰς ἄρσην, γεννῶσα πατρικῶς πάντας τοὺς ἄλλους ἀριθμούς. δεύτερον ἡ δυάς, θῆλυς ἀριθμός, ὁ δὲ αὐτὸς καὶ ἄρτιος ὑπὸ τῶν ἀριθμητικῶν καλεῖται. τρίτον ἡ τριάς, ἀριθμὸς ἄρσην: οὗτος καὶ περισσὸς ὑπὸ τῶν ἀριθμ[ητικ]ῶν νενομοθέτηται καλεῖσθαι. ἐπὶ πᾶσι δὲ τούτοις ἡ τετράς, θῆλυς ἀριθμός, ὁ δὲ αὐτὸς καὶ ἄρτιος καλεῖται, ὅτι θῆλύς ἐστιν. γεγόνασιν οὖν οἱ πάντες ἀριθμοὶ ληφθέντες ἀπὸ γένους τέσσαρες_ἀριθμὸς δ' ἦν τὸ γένος ἀόριστος_, ἀφ' ὧν ὁ τέλειος αὐτοῖς συνέστηκεν ἀριθμός, ἡ δεκάς: τὸ γὰρ ἕν, δύο, τρία, τέσσαρα γίνεται δέκα, ἐὰν ἑκάστῳ τῶν ἀριθμῶν φυλάσσηται κατ' οὐσίαν τὸ οἰκεῖον ὄνομα. ταύτην ὁ Πυθαγόρας ἔφη ἱερὰν τετρακτύν, πηγὴν ἀενάου φύσεως [ὡς] ῥιζώματ' ἔχουσαν ἐν ἑαυτῇ, καὶ ἐκ τούτου τοῦ ἀριθμοῦ πάντας ἔχειν τοὺς ἀριθμοὺς τὴν ἀρχήν: ὁ γὰρ ἕνδεκα καὶ ὁ δώδεκα καὶ οἱ λοιποὶ τὴν ἀρχὴν τοῦ εἶναι ἐκ τοῦ δέκα μετέχουσιν. ταύτης τῆς δεκάδος, τοῦ τελείου ἀριθμοῦ, τὰ τέσσαρα καλεῖται μέρη: ἀριθμός, μονάς, δύναμις, κύβος. ὧν καὶ ἐπιπλοκαὶ καὶ μίξεις πρὸς γένεσιν αὐξήσεως γίνονται, κατὰ φύσιν τὸν γόνιμον ἀριθμὸν ἀποτελοῦσαι: ὅταν γὰρ δύναμις αὐτὴ ἐφ' ἑαυτὴν κυβισθῇ, γέγονε δυναμοδύναμις: ὅταν δὲ δύναμις ἐπὶ κύβον, [γέγονε δυναμόκυβος: ὅταν δὲ κύβος ἐπὶ κύβον,> γέγονε κυβόκυβος: ὡς γίνεσθαι τοὺς πάντας ἀριθμούς, ἐξ ὧν ἡ τῶν γινομένων γένεσις γίνεται, ἑπτά: ἀριθμόν, μονάδα, δύναμιν, κύβον, δυναμοδύναμιν, δυναμόκυβον, κυβόκυβον. Οὗτος καὶ ψυχὴν ἀθάνατον εἶπε καὶ μετενσωμάτωσιν: διὸ ἔλεγεν ἑαυτὸν πρὸ μὲν τῶν Τρωϊκῶν [Αἰ]θαλίδην γεγονέναι, ἐν δὲ τοῖς Τρωϊκοῖς Ε[ὔ]φορβον, μετὰ δὲ ταῦτα Ἑρμότιμον Σάμιον, μεθ' ὃν Πύρρον Δήλιον, πέμπτον Πυθαγόραν. Διόδωρος δὲ ὁ Ἐρετριεὺς καὶ Ἀριστόξενος ὁ μουσικός φασι πρὸς Ζαράταν τὸν Χαλδαῖον ἐληλυθέναι Πυθαγόραν. τὸν δὲ ἐκθέσθαι αὐτῷ δύο εἶναι ἀπ' ἀρχῆς τοῖς οὖσιν αἴτια, πατέρα καὶ μητέρα: καὶ πατέρα μὲν φῶς, μητέρα δὲ σκότος: τοῦ δὲ φωτὸς μέρη θερμόν, ξηρόν, κοῦφον, ταχύ: τοῦ δὲ σκότους ψυχρόν, ὑγρόν, βαρύ, βραδύ: ἐκ δὲ τούτων πάντα τὸν κόσμον συνεστάναι, ἐκ θηλείας καὶ ἄρρενος. εἶναι δὲ τὸν κόσμον κατὰ φύσιν μουσικὴν ἁρμονίαν: διὸ καὶ τὸν ἥλιον ποιεῖσθαι τὴν περίοδον ἐναρμόνιον. περὶ δὲ τῶν ἐκ γῆς καὶ κόσμου γινομένων τάδε φασὶ λέγειν τὸν Ζαράταν: δύο δαίμονας εἶναι, τὸν μὲν οὐράνιον, τὸν δὲ χθόνιον: καὶ τὸν μὲν χθόνιον ἀνιέναι τὴν γένεσιν ἐκ τῆς γῆς_εἶναι γὰρ ὕδωρ_, τὸν δὲ οὐράνιον [ἐκ τοῦ κόσμου _εἶναι γὰρ] πῦρ μετέχον τοῦ ἀέρος_: θερμὸν καὶ ψυχρόν. διὸ καὶ τούτων οὐδὲν ἀναιρεῖν οὐδὲ μιαίνειν φησὶ τὴν ψυχήν: ἔστι γὰρ ταῦτα οὐσία τῶν πάντων. Κυάμους δὲ λέγεται παραγγέλλειν μὴ ἐσθίειν αἰτίᾳ τοῦ τὸν Ζαράταν εἰρηκέναι κατὰ τὴν ἀρχὴν καὶ σύγκρισιν τῶν πάντων, συνισταμένης τῆς γῆς ἔτι καὶ συνσεσημμένης, γενέσθαι [ἅμα τὸν ἄνθρωπον καὶ] τὸν κύαμον. τούτου δὲ τεκμήριόν φησιν, εἴ τις καταμασησάμενος λεῖον τὸν κύαμον καταθείη πρὸς ἥλιον χρόνον τινά_τοῦτο[ν] γὰρ εὐθέως ἀντιλήψεσθαι_, προσφέρειν ἀνθρωπίνου γόνου ὀσμήν. σαφέστερον δὲ εἶναι καὶ ἕτερον παράδειγμα λέγει: εἰ ἀνθοῦντος τοῦ κυάμου λαβόντες τὸν κύαμον καὶ τὸ ἄνθος αὐτοῦ καὶ καταθέντες εἰς χύτραν ταύτην τε καταχρίσαντες εἰς γῆν κατορύξαιμεν καὶ μετ' ὀλίγας ἡμέρας ἀνακαλύψαιμεν, ἴδοιμεν [ἂν] αὐτὸ εἶδος ἔχον τὸ μὲν πρῶτον ὡς αἰσχύνην γυναικός, μετὰ δὲ ταῦτα κατανοούμενον παιδίου κεφαλὴν συμπεφυκυῖαν. Οὗτος ἐν Κρότωνι τῆς Ἰταλίας ἅμα τοῖς μαθηταῖς ἐμπυρισθεὶς διεφθάρη. ἔθος δὲ τοῦτο ἦν παρ' αὐτῷ, ἐπειδὰν προσίῃ τις μαθητευθησόμενος, πιπράσκειν τὰ ὑπάρχοντα καὶ τὸ ἀργύριον κατατιθέναι ἐσφραγισμένον παρὰ τῷ Πυθαγόρᾳ. καὶ ὑπέμενε σιωπῶν ὁτὲ μὲν ἔτη τρία, ὁτὲ δὲ πέντε καὶ μανθάνων: αὖθις δὲ λυθεὶς ἐμίσγετο τοῖς ἑτέροις καὶ παρέμενε μαθητὴς καὶ συνειστιᾶτο ἅμα: εἰ δ' οὔ, ἀπελάμβανε τὸ ἴδιον καὶ ἀπεβάλλετο. οἱ μὲν οὖν ἐσωτερικοὶ ἐκαλοῦντο Πυθαγόρειοι, οἱ δὲ ἕτεροι Πυθαγορισταί. τῶν δὲ μαθητῶν αὐτοῦ οἱ διαφυγόντες τὸν ἐμπρησμὸν Λῦσις ἦν καὶ Ἄρχιππος καὶ ὁ τοῦ Πυθαγόρου οἰκέτης Ζάμολξις, ὃς καὶ τοὺς παρὰ Κελτοῖς Δρυΐδας λέγεται διδάξαι φιλοσοφεῖν τὴν Πυθαγόρειον φιλοσοφίαν. τοὺς δὲ ἀριθμοὺς καὶ τὰ μέτρα παρ' Αἰγυπτίων φασὶ τὸν Πυθαγόραν μαθεῖν: ὃς καταπλαγεὶς τῇ τῶν ἱερέων ἀξιοπίστῳ καὶ φαντασιώδει καὶ δυσχερῶς ἐξαγορευομένῃ σοφίᾳ, μιμησάμενος ὁμοίως καὶ αὐτὸς σιγᾶν προσέταττεν καὶ ἐν ἀδύτοις καταγ[εί]οις ἠρεμεῖν ἐποίει [τὸν] μανθάνοντα.