Sextus Empiricus, Against the Arithmeticians 3

Sextus is discussing the mathematical beliefs of the Pythagoreans.

τετρακτὺς δὲ προσηγορεύετο παρ’ αὐτοῖς ὁ ἐκ τῶν πρώτων τεσσάρων ἀριθμῶν συγκείμενος δέκα ἀριθμός. ἓν γὰρ καὶ δύο καὶ τρία καὶ τέσσαρα δέκα γίνεται· ὅς ἐστι τελειότατος ἀριθμός, ἐπείπερ ἐπ’ αὐτὸν φθάσαντες πάλιν ἀναλύομεν ἐπὶ τὴν μονάδα καὶ ἐξ ὑπαρχῆς ποιούμεθα τὰς ἀριθμήσεις. πηγήν τ’ ἀενάου φύσεως ῥιζώματ’ ἔχουσαν εἰρήκασιν αὐτὸν διὰ τὸ κατ’ αὐτοὺς ἐν αὐτῷ τὸν λόγον τῆς ἁπάντων κεῖσθαι συστάσεως, οἷον εὐθέως τοῦ τε σώματος καὶ τῆς ψυχῆς.

‘Tetraktys’ was their name for the number 10, as it is composed of the first four numbers. For 1+2+3+4=10. This is the most perfect number, since when we have arrived at it we return again to the number 1 and make our reckoning afresh. And they have called it ‘the fount which holds the roots of ever-flowing Nature’, because in it (according to them) the reason of the structure of all things resides, such as, for example, that of the body and the soul.