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On arithmetic · Arith.8–Arith.9
Ancient Greek
p. 268 Ἐκ τῶν Μοδεράτου Πυθαγορείου
Ἔστι δὲ ἀριθμός, ὡς τύπῳ εἰπεῖν, σύστημα μονάδων, ἢ προποδισμὸς πλήθους ἀπὸ μονάδος ἀρχόμενος καὶ ἀναποδισμὸς εἰς μονάδα καταλήγων. Μονάδες δὲ περαίνουσι ποσότηθ’, ἥ τις μειουμένου τοῦ πλήθους κατὰ τὴν ὑφαίρεσιν παντὸς ἀριθμοῦ στερηθεῖσα μονήν τε καὶ στάσιν λαμβάνει· περαιτέρω γὰρ ἡ μονὰς τῆς ποσότητος οὐκ ἰσχύει ἀναποδίζειν· ὥστε μονὰς ἤτοι ἀπὸ τοῦ ἑστάναι καὶ κατὰ ταὐτὰ ὡσαύτως ἄτρεπτος μένειν, ἢ ἀπὸ τοῦ διακεχωρίσθαι καὶ παντελῶς μεμονοῦσθαι τοῦ πλήθους εὐλόγως ἐκλήθη.
9 ⟨Τοῦ αὐτοῦ⟩
Τινὲς τῶν ἀριθμῶν ἀρχὴν ἀπεφήναντο τὴν μονάδα, τῶν δὲ ἀριθμητῶν ἀρχὴν τὸ ἕν. Τοῦτο δὲ σῶμα τεμνόμενον εἰς ἄπειρον· ὥστε τὰ ἀριθμητὰ τῶν ἀριθμῶν ταύτῃ διαλλάττειν, ᾗ διαφέρει τὰ σώματα τῶν ἀσωμάτων. Εἰδέναι δὲ καὶ τοῦτο χρή, ὅτι τῶν ἀριθμῶν εἰσηγήσαντο τὰς ἀρχὰς οἱ μὲν νεώτεροι τήν τε μονάδα καὶ τὴν δυάδα, οἱ δὲ Πυθαγορικοὶ πάσας παρὰ τὸ ἑξῆς τὰς τῶν ὅρων ἐκθέσεις, δι’ ὧν ἄρτιοί τε καὶ περιττοὶ νοοῦνται.
Stobaeus, Volume I: On arithmetic
p. 278 From Moderatus the Pythagorean
Number, to give a general description, is a system of monads, or the forward progression of a multitude beginning from a monad and a backward progression ending in a monad. Monads set a limit to quantity: as the multitude is diminished by subtraction, this quantity, stripped of every number, reaches a state of rest and stands still. For the monad cannot move backward any farther along the scale of quantity. It was therefore reasonably called a “monad,” either because it stands still and remains unchanged, always in the same condition, or because it has been separated from the multitude and left altogether alone.23
9 ⟨The same author⟩
Some declared the monad to be the beginning of numbers, but the One the beginning of things that are numbered. The latter is a body divisible without limit; thus things that are numbered differ from numbers in the same way that bodies differ from incorporeal things. We should also know that, as principles of numbers, later thinkers introduced the monad and the dyad, whereas the Pythagoreans introduced the successive setting out of all the terms through which even and odd are understood.24
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Reading Stobaeus, Volume I · On arithmetic · Arith.8–Arith.9
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Stobaeus gathered Greek philosophy and poetry for his son Septimius. Volume I presents the dedication testimony, On Arithmetic, Book I through chapter 60, and the ancient contents of all four books. This complete bilingual edition includes an introduction and 2,117 explanatory notes.
Historical Text and Translation
The Greek follows Curt Wachsmuth’s 1884 Volume I, checked against the supplied scan. Gaps, lost-chapter headings, and uncertain attributions remain visible. Chapter 2 includes a labeled proposed reconstruction. The appendix outlines Books I–IV; the full texts of Books II–IV are outside this volume. Reader pages preserve the companion PDF’s numbering.
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