Refutation of All Heresies 6.23.3
Authorship disputed: The work names no author. Book 1 was long printed among Origen's works as the Philosophumena; after books 4–10 were found in a manuscript from Mount Athos (published 1851), it was assigned to Hippolytus, the usual view today, though some scholars ascribe it to another Roman writer of the same circle. Books 2 and 3 are lost, and book 4 lacks its beginning.
Summary: For Pythagoras ten is the perfect number, bodies arise from point, line, and surface, and the tetraktys (1+2+3+4=10) generates the perfect number.
Greek text · Duncker–Schneidewin, 260–262
Τοῦτον γὰρ οἶδε μόνον τέλειον ἀριθμὸν Πυθαγόρας τὸν δέκα· τὸν γὰρ ἕνδεκα καὶ δώδεκα προσθήκην καὶ ἐπαναποδισμὸν τῆς δεκάδος, οὐκ ἄλλου τινὸς ἀριθμοῦ γέννησιν τὸ προστιθέμενον. Πάντα δὲ σώματα στερεὰ ἐξ ἀσωμάτων γεννᾷ. Τῶν τε γὰρ σωμάτων καὶ ἀσωμάτων ὁμοῦ στοιχεῖον εἶναι φησὶ καὶ ἀρχὴν τὸ σημεῖον ὅ ἐστιν ἀμερές, γίνεται δὲ, φησίν, ἐκ σημείου γραμμή, καὶ [ἐκ γραμμῆς ἐπιφάνεια], ἐπιφάνεια δὲ ῥυεῖσα εἰς βάθος στερεὸν ὑφέστηκε, φησί, σῶμα. Ὅθεν καὶ ὅρκος τίς ἐστι τοῖς Πυθαγορικοῖς ἡ τῶν τεσσάρων στοιχείων συμφωνία. Ὀμνύουσι δʼ οὕτως· Ναὶ μὰ τὸν ἁμετέρᾳ κεφαλᾴ παραδόντα τετρακτύν, Πηγὴν ἀενάου φύσεως [ῥιζώματ᾿] ἔχουσαν. Ἔστι δὲ ἡ τετρακτὺς τῶν φυσικῶν καὶ στερεῶν σωμάτων ἀρχή, ὡς ἡ μονὰς τῶν νοητῶν. Ὅτι δὲ καὶ ἡ τετρακτὺς γεννᾷ, φησί, τὸν τέλειον ἀριθμόν, ὡς ἐν τοῖς νοητοῖς [ἡ μονάς], τὸν δέκα, διδάσκουσιν οὕτως. Εἰ ἀρξάμενος ἀριθμεῖν λέγει τις ὅτι ἕν, καὶ ἐπιφέρει δύο, ἔπειτα ὁμοίως τρία, ἔσονται ταῦτα ἕξ· πρὸς δὲ τούτοις ἔτι τέσσαρα, ἔσται ὁμοίως τὸ πᾶν δέκα. Τὸ γὰρ ἕν, δύο, τρία, τέσσαρα γίνεται δέκα, ὁ τέλειος ἀριθμός. Οὕτως, φησί, κατὰ πάντα ἐμιμήσατο ἡ τετρακτὺς τὴν νοητὴν μονάδα, τέλειον ἀριθμὸν γεννῆσαι δυνηθεῖσαν.
English · Claude translation
For Pythagoras knows only this number, ten, as perfect; for eleven and twelve are an addition to and repetition of the decad, and what is added is not the generation of any other number. And he generates all solid bodies from incorporeal things. For he says that the element and principle of both bodies and incorporeals together is the point, which is without parts; from a point, he says, comes a line, [from a line a surface], and a surface flowing into depth becomes, he says, a solid body. Hence the Pythagoreans also have an oath, the concord of the four elements. They swear thus: “Yes, by him who handed to our head the tetraktys, a spring holding [the roots] of ever-flowing nature.” The tetraktys is the principle of natural and solid bodies, as the monad is of intelligibles. And that the tetraktys, as [the monad] among the intelligibles, also generates, he says, the perfect number, ten, they teach thus: if someone beginning to count says one, and adds two, and then likewise three, these will be six; and adding to these four more, the whole will likewise be ten. For one, two, three, four make ten, the perfect number. So, he says, the tetraktys imitated in every respect the intelligible monad, being able to generate a perfect number.
About this passage
Notes
Translation notes
- The oath is from the Pythagorean Golden Verses 47–48. The bracketed words are the editor's supplements.
Notes on the original text
- Digital text corrected (stray punctuation in the digital text; wrong accent and breathing in the digital text; wrong accent in the digital text): τὴς δεκάδος → τῆς δεκάδος; ἀσωμάτων· ὁμοῦ → ἀσωμάτων ὁμοῦ; Εἵ ἀρξάμενος → Εἰ ἀρξάμενος.
Cite this passage
Hippolytus, Haer. 6.23.3 (trans. Sophia Scriptura, https://sophiascriptura.com/fathers/hippolytus-refutatio/6/23/3/).
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Plain text
Hippolytus, Haer. 6.23.3 (trans. Sophia Scriptura, https://sophiascriptura.com/fathers/hippolytus-refutatio/6/23/3/).
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