§13.8#3ἔτι ἄτοπον εἰ ὁ ἀριθμὸς ὁ μέχρι τῆς δεκάδος μᾶλλόν τι ὂν καὶ εἶδος αὐτῆς τῆς δεκάδος, καίτοι τοῦ μὲν οὐκ ἔστι γένεσις ὡς ἑνός, τῆς δʼ ἔστιν.
Moreover, it is absurd if the number up to the Decad is more of a being and a form than the Decad itself, although of the former there is no generation as a single thing, whereas of the latter there is.
πειρῶνται δʼ ὡς τοῦ μέχρι τῆς δεκάδος τελείου ὄντος ἀριθμοῦ.
And they try to argue on the assumption that the number up to the Decad is complete.
γεννῶσι γοῦν τὰ ἑπόμενα, οἷον τὸ κενόν, ἀναλογίαν, τὸ περιττόν, τὰ ἄλλα τὰ τοιαῦτα, ἐντὸς τῆς δεκάδος· τὰ μὲν γὰρ ταῖς ἀρχαῖς ἀποδιδόασιν, οἷον κίνησιν στάσιν, ἀγαθὸν κακόν, τὰ δʼ ἄλλα τοῖς ἀριθμοῖς· διὸ τὸ ἓν τὸ περιττόν· εἰ γὰρ ἐν τῇ τριάδι, πῶς ἡ πεντὰς περιττόν;
At any rate, they generate the consequences, such as the void, proportion, the odd, and other such things, within the Decad; for some things they attribute to the principles, such as motion and rest, good and bad, and other things to numbers; which is why the One is the odd; for if it is in the Triad, how is the Pentad odd?
ἔτι τὰ μεγέθη καὶ ὅσα τοιαῦτα μέχρι ποσοῦ, οἷον ἡ πρώτη γραμμή, ἡ ἄτομος, εἶτα δυάς, εἶτα καὶ ταῦτα μέχρι δεκάδος. —ἔτι εἰ ἔστι χωριστὸς ὁ ἀριθμός, ἀπορήσειεν ἄν τις πότερον πρότερον τὸ ἓν ἢ ἡ τριὰς καὶ ἡ δυάς.
Moreover, up to what limit do magnitudes and all such things go, for example, the first line, the indivisible one, then the Dyad, then these also up to the Decad? —Moreover, if number is separable, one might puzzle whether the One is prior, or the Triad and the Dyad.
ᾗ μὲν δὴ σύνθετος ὁ ἀριθμός, τὸ ἕν, ᾗ δὲ τὸ καθόλου πρότερον καὶ τὸ εἶδος, ὁ ἀριθμός· ἑκάστη γὰρ τῶν μονάδων μόριον τοῦ ἀριθμοῦ ὡς ὕλη, ὁ δʼ ὡς εἶδος.
Insofar as number is composite, the One [is prior], but insofar as the universal and the form are prior, number is; for each of the units is a part of number as matter, and the latter is as form.
καὶ ἔστι μὲν ὡς ἡ ὀρθὴ προτέρα τῆς ὀξείας, ὅτι ὥρισται καὶ τῷ λόγῳ· ἔστι δʼ ὡς ἡ ὀξεῖα, ὅτι μέρος καὶ εἰς ταύτην διαιρεῖται.
And in one way the right angle is prior to the acute angle, because it is defined and also prior in definition; but in another way the acute angle is, because it is a part and the right angle is divided into it.
ὡς μὲν δὴ ὕλη ἡ ὀξεῖα καὶ τὸ στοιχεῖον καὶ ἡ μονὰς πρότερον, ὡς δὲ κατὰ τὸ εἶδος καὶ τὴν οὐσίαν τὴν κατὰ τὸν λόγον ἡ ὀρθὴ καὶ τὸ ὅλον τὸ ἐκ τῆς ὕλης καὶ τοῦ εἴδους· ἐγγύτερον γὰρ τοῦ εἴδους καὶ οὗ ὁ λόγος τὸ ἄμφω, γενέσει δʼ ὕστερον.
As matter, then, the acute angle, the element, and the unit are prior; but as regards form and substance according to definition, the right angle and the whole composed of matter and form are prior; for that which is composed of both is nearer to the form and to that of which there is a definition, though posterior in generation.
πῶς οὖν ἀρχὴ τὸ ἕν;
How, then, is the One a principle?
ὅτι οὐ διαιρετόν, φασίν· ἀλλʼ ἀδιαίρετον καὶ τὸ καθόλου καὶ τὸ ἐπὶ μέρους καὶ τὸ στοιχεῖον.
"Because it is indivisible," they say; but the universal, the particular, and the element are also indivisible.
ἀλλὰ τρόπον ἄλλον, τὸ μὲν κατὰ λόγον τὸ δὲ κατὰ χρόνον.
But they are so in a different way, the one in definition and the other in time.
ποτέρως οὖν τὸ ἓν ἀρχή;
In which of the two ways, then, is the One a principle?
ὥσπερ γὰρ εἴρηται, καὶ ἡ ὀρθὴ τῆς ὀξείας καὶ αὕτη ἐκείνης δοκεῖ προτέρα εἶναι, καὶ ἑκατέρα μία.
For as has been said, both the right angle seems to be prior to the acute angle and the latter to the former, and each is one.
ἀμφοτέρως δὴ ποιοῦσι τὸ ἓν ἀρχήν.
Thus they make the One a principle in both ways.
ἔστι δὲ ἀδύνατον· τὸ μὲν γὰρ ὡς εἶδος καὶ ἡ οὐσία τὸ δʼ ὡς μέρος καὶ ὡς ὕλη.
But this is impossible; for the one is as form and substance, and the other as part and as matter.
ἔστι γάρ πως ἓν ἑκάτερον—τῇ μὲν ἀληθείᾳ δυνάμει (εἴ γε ὁ ἀριθμὸς ἕν τι καὶ μὴ ὡς σωρὸς ἀλλʼ ἕτερος ἐξ ἑτέρων μονάδων, ὥσπερ φασίν), ἐντελεχείᾳ δʼ οὔ, ἔστι μονὰς ἑκατέρα·
For each is in a way one—in truth potentially (if indeed number is some one thing and not like a heap, but different [composed] of different units, as they say), but not actually, [for then] each is a unit.
αἴτιον δὲ τῆς συμβαινούσης ἁμαρτίας ὅτι ἅμα ἐκ τῶν μαθημάτων ἐθήρευον καὶ ἐκ τῶν λόγων τῶν καθόλου, ὥστʼ ἐξ ἐκείνων μὲν ὡς στιγμὴν τὸ ἓν καὶ τὴν ἀρχὴν ἔθηκαν (ἡ γὰρ μονὰς στιγμὴ ἄθετός ἐστιν· καθάπερ οὖν καὶ ἕτεροί τινες ἐκ τοῦ ἐλαχίστου τὰ ὄντα συνετίθεσαν, καὶ οὗτοι, ὥστε γίγνεται ἡ μονὰς ὕλη τῶν ἀριθμῶν, καὶ ἅμα προτέρα τῆς δυάδος, πάλιν δʼ ὑστέρα ὡς ὅλου τινὸς καὶ ἑνὸς καὶ εἴδους τῆς δυάδος οὔσης)· διὰ δὲ τὸ καθόλου ζητεῖν τὸ κατηγορούμενον ἓν καὶ οὕτως ὡς μέρος ἔλεγον.
The cause of the resulting error is that they were searching at once from mathematics and from universal arguments, so that from the former they set up the One as a point and a principle (for the unit is a point without position; just as some others composed the existents from the least, so also did these, so that the unit becomes the matter of numbers, and at the same time prior to the Dyad, but again posterior to the Dyad as being some whole, one, and form); and because of searching universally, they spoke of the predicated One as being in this way also a part.
ταῦτα δʼ ἅμα τῷ αὐτῷ ἀδύνατον ὑπάρχειν.
But it is impossible for these to belong to the same thing at the same time.
εἰ δὲ τὸ ἓν αὐτὸ δεῖ †μόνον ἄθετον† εἶναι (οὐθενὶ γὰρ διαφέρει ἢ ὅτι ἀρχή), καὶ ἡ μὲν δυὰς διαιρετὴ ἡ δὲ μονὰς οὔ, ὁμοιοτέρα ἂν εἴη τῷ ἑνὶ αὐτῷ ἡ μονάς.
If indeed the One itself must be †only without position† (for it differs in nothing else than in being a principle), and the Dyad is divisible while the unit is not, the unit would be more similar to the One itself.
εἰ δʼ ἡ μονάς, κἀκεῖνο τῇ μονάδι ἢ τῇ δυάδι· ὥστε προτέρα ἂν εἴη ἑκατέρα ἡ μονὰς τῆς δυάδος.
And if the unit is [similar to it], that [the One itself] also is [similar] to the unit rather than to the Dyad; so that in each way the unit would be prior to the Dyad.
οὔ φασι δέ· γεννῶσι γοῦν τὴν δυάδα πρῶτον.
But they do not say so; at any rate, they generate the Dyad first.
ἔτι εἰ ἔστιν ἡ δυὰς ἕν τι αὐτὴ καὶ ἡ τριὰς αὐτή, ἄμφω δυάς.
Moreover, if the Dyad itself is some one thing, and the Triad itself is, both together are a dyad.
ἐκ τίνος οὖν αὕτη ἡ δυάς;
From what, then, does this dyad come?