§3.4#2ὅτι μὲν οὖν προσήκουσα τοῖς φυσικοῖς ἡ θεωρία, δῆλον ἐκ τούτων.
\nIt is clear, then, from these things that the investigation is appropriate for the students of nature.
εὐλόγως δὲ καὶ ἀρχὴν αὐτὸ τιθέασι πάντες· οὔτε γὰρ μάτην οἷόν τε αὐτὸ εἶναι, οὔτε ἄλλην ὑπάρχειν αὐτῷ δύναμιν πλὴν ὡς ἀρχήν· ἅπαντα γὰρ ἢ ἀρχὴ ἢ ἐξ ἀρχῆς.
And it is with good reason that all posit it as a principle; for it is not possible for it to exist in vain, nor can any other power belong to it except as a principle; for everything is either a principle or from a principle.
τοῦ δὲ ἀπείρου οὐκ ἔστιν ἀρχή· εἴη γὰρ ἂν αὐτοῦ πέρας.
But of the infinite there is no principle; for [if there were] there would be a limit of it.
ἔτι δὲ καὶ ἀγένητον καὶ ἄφθαρτον ὡς ἀρχή τις οὖσα· τό τε γὰρ γενόμενον ἀνάγκη τέλος λαβεῖν, καὶ τελευτὴ πάσης ἔστιν φθορᾶς.
Moreover, it is also ungenerated and indestructible, as being a kind of principle; for what has come to be must of necessity reach an end, and there is an end of every passing away.
διό, καθάπερ λέγομεν, οὐ ταύτης ἀρχή, ἀλλʼ αὕτη τῶν ἄλλων εἶναι δοκεῖ καὶ περιέχειν ἅπαντα καὶ πάντα κυβερνᾶν, ὥς φασιν ὅσοι μὴ ποιοῦσι παρὰ τὸ ἄπειρον ἄλλας αἰτίας, οἷον νοῦν ἢ φιλίαν·
Therefore, as we say, there is no principle of this, but this seems to be [the principle] of other things, and to encompass all things and steer all things, as they say who do not posit other causes besides the infinite, such as Intellect or Friendship.
καὶ τοῦτʼ εἶναι τὸ θεῖον· ἀθάνατον γὰρ καὶ ἀνώλεθρον, ὥσπερ φησὶν Ἀναξίμανδρος καὶ οἱ πλεῖστοι τῶν φυσιολόγων.
And this is the divine; for it is immortal and indestructible, as Anaximander says and most of the physicists.
τοῦ δʼ εἶναί τι ἄπειρον ἡ πίστις ἐκ πέντε
μάλιστʼ ἂν συμβαίνοι σκοποῦσιν, ἔκ τε τοῦ χρόνου (οὗτος γὰρ ἄπειρος) καὶ ἐκ τῆς ἐν τοῖς μεγέθεσι διαιρέσεαως (χρῶνται γὰρ καὶ οἱ μαθηματικοὶ τῷ ἀπείρῳ)· ἔτι τῷ οὕτως ἂν μόνως μὴ ὑπολείπειν γένεσιν καὶ φθοράν, εἰ ἄπειρον εἴη ὅθεν ἀφαιρεῖται τὸ γιγνόμενον· ἔτι τῷ τὸ πεπερασμένον ἀεὶ πρός τι περαίνειν, ὥστε ἀνάγκη μηδὲν εἶναι πέρας, εἰ ἀεὶ περαίνειν ἀνάγκη ἕτερον πρὸς ἕτερον.
\nBelief in the existence of something infinite would arise for those who consider it chiefly from five things: first, from time (for this is infinite); second, from division in magnitudes (for mathematicians also use the infinite); further, because only in this way would generation and destruction not fail, if that from which what is generated is taken were infinite; further, because the finite is always limited against something, so that of necessity there is no [ultimate] limit, if it is always necessary for one thing to be limited against another.
μάλιστα δὲ καὶ κυριώτατον, ὃ τὴν κοινὴν ποιεῖ ἀπορίαν πᾶσι· διὰ γὰρ τὸ ἐν τῇ νοήσει μὴ ὑπολείπειν καὶ ὁ ἀριθμὸς δοκεῖ ἄπειρος εἶναι καὶ τὰ μαθηματικὰ μεγέθη καὶ τὸ ἔξω τοῦ οὐρανοῦ.
And most of all and most authoritative, which creates the common difficulty for all; for because of not failing in thought, number also seems to be infinite, and mathematical magnitudes, and what is outside the heaven.
ἀπείρου δʼ ὄντος τοῦ ἔξω, καὶ σῶμα ἄπειρον εἶναι δοκεῖ καὶ κόσμοι· τί γὰρ μᾶλλον τοῦ κενοῦ ἐνταῦθα ἢ ἐνταῦθα; ὥστʼ εἴπερ μοναχοῦ, καὶ πανταχοῦ εἶναι τὸν ὄγκον.
And what is outside being infinite, there also seems to be an infinite body and worlds; for why [should there be] void here rather than there? so that if [there is a bulk] in one place, the bulk must also be everywhere.
ἅμα δʼ εἰ καὶ ἔστι κενὸν καὶ τόπος ἄπειρος, καὶ σῶμα εἶναι ἀναγκαῖον· ἐνδέχεσθαι γὰρ ἢ εἶναι οὐδὲν διαφέρει ἐν τοῖς ἀϊδίοις. ἔχει
δʼ ἀπορίαν ἡ περὶ τοῦ ἀπείρου θεωρία·
And at the same time, even if there is void and infinite space, there must also be body; for in eternal things, to be possible and to be do not differ at all.\nBut the study of the infinite has difficulty; for to those who posit that it does not exist, and to those who posit that it does, many impossible things happen.
καὶ γὰρ μὴ εἶναι τιθεμένοις πόλλʼ ἀδύνατα συμβαίνει καὶ εἶναι. ἔτι δὲ ποτέρως ἔστιν, πότερον ὡς οὐσία ἢ ὡς συμβεβηκὸς καθʼ αὐτὸ φύσει τινί;
And further, in which way does it exist: as a substance or as an accident in itself to some nature?
ἢ οὐδετέρως, ἀλλʼ οὐδὲν ἦττον ἔστιν ἄπειρον ἢ ἄπειρα τῷ πλήθει;
Or in neither way, but nonetheless is there an infinite, or infinites in multitude?
μάλιστα δὲ φυσικοῦ ἐστιν σκέψασθαι εἰ ἔστι μέγεθος αἰσθητὸν ἄπειρον.
But it is especially for the physicist to examine whether there is a sensible infinite magnitude.
πρῶτον οὖν διοριστέον ποσαχῶς λέγεται τὸ ἄπειρον.
First, then, we must distinguish in how many ways the infinite is spoken of.
ἕνα μὲν δὴ τρόπον τὸ ἀδύνατον διελθεῖν τῷ μὴ πεφυκέναι διιέναι, ὥσπερ ἡ φωνὴ ἀόρατος· ἄλλως δὲ τὸ διέξοδον ἔχον ἀτελεύτητον, ἢ ὃ μόγις, ἢ ὃ πεφυκὸς ἔχειν μὴ ἔχει διέξοδον ἢ. πέρας.
In one way, indeed, it is what is impossible to go through because of not being of a nature to be gone through, just as voice is invisible; and in another way, what has a passage but without end, or what [can be gone through] with difficulty, or what, being of a nature to have [a passage or limit], does not have a passage or a limit.
ἔτι ἄπειρον ἅπαν ἢ κατὰ πρόσθεσιν ἢ κατὰ διαίρεσιν ἢ ἀμφοτέρως.
Further, every infinite is so either by addition or by division, or both.