27. On these points it is not necessary to discourse any longer in this place. For whatever cause a man supposes shall produce such passions and changes, that very cause will contain each of these worlds in itself; because each of them has its sea and land, each its proper middle, and each its passions and change of bodies, and the nature and power which contain and preserve each in its place and being. For that which is without, whether it be nothing at all or an infinite vacuum, cannot allow any middle, as we have already said. But there being several worlds, each has its proper middle apart; so that in each of them there will be motions proper to bodies, some tending down to the midst, others mounting aloft from the midst, others moving round about it, according as they themselves do distinguish motions. And he who asserts there are many middles, and that heavy bodies from all sides do tend unto one alone, is like to him who shall affirm that the blood of several men runs from all parts into one vein, or that all their brains should be contained within one and the same membrane; supposing it absurd, that all natural bodies which are solid should not be in one place, and the rare in another. He that thus thinketh is certainly a mean philosopher; and no better is he who will not allow the whole to have all parts in their order, rank, and natural situation. What could be more foolish, than for a man to call that a world which had a moon within it so situated, as if a man should have his brains in his heels, and his heart in his forehead? Whereas there is no absurdity or inconveniency, if, in supposing several distinct worlds separated from one another, a man should distinguish and separate their parts. For in each of them the earth, sea, and sky will be placed and situated in their proper places, and each of these worlds may have its superior, inferior, circular, and middle part, not in respect of another world, nor in reference to what is without, but to what is within itself.
27. περὶ ὧν οὐκ ἀναγκαῖον ἐνταῦθα πλείοσι λόγοις χρῆσθαι. ἣν γὰρ ἄν τις ὑπόθηται τῶν παθῶν τούτων καὶ τῶν μεταβολῶν αἰτίαν εἶναι δημιουργόν, αὕτη συνέξει τῶν κόσμων ἕκαστον ἐν ἑαυτῷ. καὶ γὰρ γῆν καὶ θάλατταν ἕκαστος ἔχει κόσμος· ἔχει γὰρ καὶ μέσον ἕκαστος ἴδιον, καὶ πάθη σωμάτων καὶ μεταβολὰς καὶ φύσιν καὶ δύναμιν, ἣ σῴζει καὶ φυλάττει κατὰ χώραν ἕκαστον. τὸ μὲν γὰρ ἐκτός, εἴτʼ οὐδέν ἐστιν εἴτε κενὸν ἄπειρον, οὐ παρέχει μέσον, ὡς εἴρηται· πλειόνων δὲ κόσμων ὄντων, καθʼ ἕκαστόν ἐστιν ἴδιον μέσον· ὥστε κίνησις ἰδία τοῖς μὲν ἐπὶ τοῦτο τοῖς δʼ ἀπὸ τούτου τοῖς δὲ περὶ τοῦτο, καθάπερ αὐτοὶ διαιροῦσιν. ὁ δʼ ἀξιῶν, πολλῶν μέσων ὄντων, ἐφʼ ἓν μόνον ὠθεῖσθαι τὰ βάρη πανταχόθεν, οὐδὲν διαφέρει τοῦ, πολλῶν ὄντων ἀνθρώπων, ἀξιοῦντος εἰς μίαν φλέβα τὸ πανταχόθεν αἷμα συρρεῖν καὶ μιᾷ μήνιγγι τοὺς πάντων ἐγκεφάλους περιέχεσθαι, δεινὸν ἡγούμενος, εἰ τῶν φυσικῶν σωμάτων οὐ μίαν ἅπαντα τὰ στερρὰ καὶ μίαν τὰ μανὰ χώραν ἐφέξει. καὶ γὰρ οὗτος ἄτοπος ἔσται κἀκεῖνος ἀγανακτῶν, εἰ τὰ ὅλα τοῖς αὑτῶν μέρεσι χρῆται, τὴν κατὰ φύσιν θέσιν ἔχουσιν ἐν ἑκάστῳ καὶ τάξιν. ἐκεῖνο γὰρ ἦν ἄτοπον, εἴ τις ἔλεγε κόσμον εἶναι τὸν ἐν αὐτῷ σελήνην ἔχοντα καθάπερ ἄνθρωπον ἐν ταῖς πτέρναις τὸν ἐγκέφαλον φοροῦντα καὶ τὴν καρδίαν ἐν τοῖς κροτάφοις. τὸ δὲ πλείονας ποιοῦντας χωρὶς ἀλλήλων κόσμους ἅμα τοῖς ὅλοις τὰ μέρη συναφορίζειν καὶ συνδιαιρεῖν οὐκ ἄτοπον· ἡ γὰρ ἐν ἑκάστῳ γῆ καὶ θάλασσα καὶ οὐρανὸς κείσεται κατὰ φύσιν ὡς προσήκει, τὸ τʼ ἄνω καὶ κάτω καὶ κύκλῳ καὶ μέσον οὐ πρὸς ἄλλον οὐδʼ ἐκτὸς ἀλλʼ ἐν ἑαυτῷ καὶ πρὸς ἑαυτὸν ἔχει τῶν κόσμων ἕκαστος.
28. And as to the argument which some do draw from a stone supposed to be placed without the world, it neither proves rest nor motion; for how could it remain suspended, seeing it is by nature heavy, or move towards the midst of the world, as other ponderous bodies, seeing it is neither part of it nor like it? And as to that earth which is fixed and environed by another world, we must not wonder, considering its weightiness, if it does not drop down, seeing it is upheld by a certain natural force pertaining to it. For if we shall take high and low not within the world but without, we shall find ourselves involved in the same difficulties as Epicurus was when he made his little indivisible atoms to move and tend to those places which are under foot, as if the vacuum had feet, or its infinite space would permit one to talk of high or low. Indeed, a man would marvel what should cause Chrysippus to say, that the world was placed and situated directly in the midst, and that the matter thereof, from all eternity having possessed itself of the midst, yet is so compacted together that it remains for ever. For he writes this in his Fourth Book of Possible Things, vainly imagining there is a middle in that vast emptiness, and still more absurdly attributing unto that middle, which is not, the cause of the world’s stability and continuance; he having often said in other writings of his that the substance is upheld and governed, partly by the motions tending to the midst of it, and partly by others parting from the midst of it.
28. ὃν μὲν γὰρ ἔξω τοῦ κόσμου λίθον ὑποτίθενταί τινες οὔτε μονῆς εὐπόρως παρέχει νόησιν οὔτε κινήσεως. πῶς γὰρ ἢ μενεῖ βάρος ἔχων ἢ κινήσεται πρὸς τὸν κόσμον, ὥσπερ τὰ λοιπὰ βάρη, μήτε μέρος ὢν αὐτοῦ μήτε συντεταγμένος εἰς τὴν οὐσίαν; γῆν δʼ ἐν ἑτέρῳ κόσμῳ περιεχομένην καὶ συνδεδεμένην οὐκ ἔδει διαπορεῖν ὅπως οὐκ ἐνταῦθα μεταχωρεῖ διὰ βάρος ἀπορραγεῖσα τοῦ ὅλου, τὴν φύσιν ὁρῶντας καὶ τὸν τόνον ὑφʼ οὗ συνέχεται τῶν μερῶν ἕκαστον. ἐπεὶ μὴ πρὸς τὸν κόσμον ἀλλʼ ἐκτὸς αὐτοῦ τὸ κάτω καὶ ἄνω λαμβάνοντες, ἐν ταῖς αὐταῖς ἀπορίαις Ἐπικούρῳ γενησόμεθα κινοῦντι τὰς ἀτόμους ἁπάσας εἰς τοὺς ὑπὸ πόδας τόπους, ὥσπερ ἢ τοῦ κενοῦ πόδας ἔχοντος ἢ τῆς ἀπειρίας ἐν αὑτῇ κάτω τε καὶ ἄνω νοῆσαι διδούσης, διὸ καὶ Χρύσιππον ἔστι θαυμάζειν, μᾶλλον δʼ ὅλως διαπορεῖν, ὅ τι δὴ παθὼν τὸν κόσμον ἐν μέσῳ φησὶν ἱδρῦσθαι, καὶ τὴν οὐσίαν αὐτοῦ τὸν μέσον τόπον ἀιδίως κατειληφυῖαν, οὐχ ἥκιστα τούτῳ συνείργεσθαι πρὸς διαμονὴν καὶ οἱονεὶ ἀφθαρσίαν. ταυτὶ γὰρ ἐν τῷ τετάρτῳ περὶ Δυνατῶν λέγει, μέσον τε τοῦ ἀπείρου τόπον οὐκ ὀρθῶς ὀνειρώττων ἀτοπωτέραν τε τῆς διαμονῆς τοῦ κόσμου τῷ ἀνυπάρκτῳ μέσῳ τὴν αἰτίαν ὑποτιθείς· καὶ ταῦτα πολλάκις εἰρηκὼς ἑτέροις, ὅτι ταῖς εἰς τὸ αὑτῆς μέσον ἡ οὐσία καὶ ταῖς ἀπὸ τοῦ αὑτῆς μέσου διοικεῖται καὶ συνέχεται κινήσεσι.
29. As to the other oppositions which the Stoics make, who should fear them? As when they demand, how it is possible to maintain a fatal destiny and a divide providence, and how it can be otherwise but that we must admit of several Jupiters, when we assert the plurality of worlds. Now if there be an inconveniency in admitting many Jupiters, their opinions will appear far more absurd; for they imagine there are suns, and moons, Apollos, Dianas, and Neptunes innumerable, in innumerable changes and revolutions of worlds. But where is the necessity which lies upon us to grant that there must be many Jupiters if there be many worlds, seeing that each of them may be subject to a sovereign governor of the whole, a God endued with a suitable mind and ability, like to him whom we name the Lord and Father of all things? Or what shall hinder us from asserting that the several worlds must be subject to the providence and destiny of Jupiter, and that he has an eye to all things, directing all, and administering to them the principles, seeds, and causes of all things which are made? For, while we often see here a body composed of several other distinct bodies,—for example, the assembly of a town, an army, or a chorus,— in each of which bodies there is life, prudence, and understanding; so it cannot be impossible that, in the whole universe, ten or fifty or a hundred worlds which may be in it should all use the same reason, and all correspond with the same principle. For this order and disposition is very suitable to the Gods; for we must not make them kings of a swarm of bees who never stir out of their hives, or keep them fast imprisoned in matter, like those who affirm the Gods to be certain dispositions of the air, and powers of waters and fire, infused and mixed within, which arise and spring up together with the world, and in time are to be burnt and end with it,—not affording them the liberty of coachmen and pilots, but nailing them down to their bases like statues and images. For they enclose the Gods within matter, and that in so strict a manner as makes them liable to all the changes, alterations, and decays of it.
29. καὶ μὴν τὰ γʼ ἄλλα τῶν Στωικῶν τίς ἂν φοβηθείη, πυνθανομένων πῶς εἱμαρμένη μία μενεῖ καὶ πρόνοια, καὶ οὐ πολλοὶ Δίες καὶ Ζῆνες ἔσονται, πλειόνων ὄντων κόσμων; πρῶτον μὲν γὰρ εἰ τὸ πολλοὺς εἶναι Δίας καὶ Ζῆνας ἄτοπόν ἐστι, πολλῷ δήπουθεν ἔσται τὰ ἐκείνων ἀτοπώτερα· καὶ γὰρ ἡλίους καὶ σελήνας καὶ Ἀπόλλωνας καὶ Ἀρτέμιδας καὶ Ποσειδῶνας ἐν ἀπείροις κόσμων περιόδοις ἀπείρους ποιοῦσιν. ἔπειτα τίς ἀνάγκη πολλοὺς εἶναι Δίας, ἂν πλείονες ὦσι κόσμοι, καὶ μὴ καθʼ ἕκαστον ἄρχοντα πρῶτον καὶ ἡγεμόνα τοῦ ὅλου θεὸν ἔχοντα καὶ νοῦν καὶ λόγον, οἷος ὁ παρʼ ἡμῖν κύριος ἁπάντων καὶ πατὴρ ἐπονομαζόμενος; ἢ τί κωλύσει τῆς τοῦ Διὸς εἱμαρμένης καὶ προνοίας ὑπηκόους πάντας εἶναι, καὶ τοῦτον ἐφορᾶν ἐν μέρει καὶ κατευθύνειν, ἐνδιδόντα πᾶσιν ἀρχὰς καὶ σπέρματα καὶ λόγους τῶν περαινομένων; οὐ γὰρ ἐνταῦθα μὲν ἓν συνίσταται σῶμα πολλάκις ἐκ διεστώτων σωμάτων, οἷον ἐκκλησία καὶ στράτευμα καὶ χορός· ὧν ἑκάστῳ καὶ ζῆν καὶ φρονεῖν καὶ μανθάνειν συμβέβηκεν, ὡς οἴεται Χρύσιππος· ἐν δὲ τῷ παντὶ δέκα κόσμους ἢ πεντήκοντʼ ἢ ἑκατὸν ὄντας ἑνὶ χρῆσθαι λόγῳ καὶ πρὸς ἀρχὴν συντετάχθαι μίαν ἀδύνατόν ἐστιν. ἀλλὰ καὶ πάνυ πρέπει θεοῖς ἡ τοιαύτη διάταξις· οὐ γὰρ ὡς σμήνους ἡγεμόνας δεῖ ποιεῖν ἀνεξόδους οὐδὲ φρουρεῖν συγκλείσαντας τῇ ὕλῃ μᾶλλον δὲ συμφράξαντας, ὥσπερ οὗτοι τοὺς θεοὺς ἀέρων ἕξεις ποιοῦντες καὶ ὑδάτων καὶ πυρὸς δυνάμεις ἐγκεκραμένας ἡγούμενοι συγγεννῶσι τῷ κόσμῳ καὶ πάλιν συγκατακάουσιν, οὐκ ἀπολύτους οὐδʼ ἐλευθέρους οἷον ἡνιόχους ἢ κυβερνήτας ὄντας ἀλλʼ, ὥσπερ ἀγάλματα προσηλοῦται καὶ συντήκεται βάσεσιν, οὕτως ἐγκεκλειμένους εἰς τὸ σωματικὸν καὶ συγκαταγεγομφωμένους, κοινωνοῦντας αὐτῷ μέχρι φθορᾶς καὶ διαλύσεως ἁπάσης καὶ μεταβολῆς.
30. It is certainly more agreeable to the nature of the Gods to say that they are wholly at liberty, like Castor and Pollux, ready to succor such as are overtaken by bad weather at sea; for when they appear, the winds cease and the waves are calmed. Not that they navigate and are partakers of the same peril; but they only appear in the sky, and the danger is over. Thus do the Gods visit each world, and rule and provide for all things in them. Jupiter in Homer cast not his eyes far from the city of Troy into Thrace, and to the nomad Scythians along the river Ister; but the true Jupiter has several seemly and agreeable passages for his majesty from one world into another, not looking into the infinite vacuum without, nor regarding himself and nothing else, as some have imagined, but weighing the deeds of Gods and men, and the motions and revolutions of the stars. For the Divinity does not hate variety and changes, but takes great pleasure in them, as one may conjecture by the circuits, conversions, and mutations observable in the heavens. And therefore I conclude that the infinite number of worlds is a chimera, which has not the least probability of truth, and which cannot by any means admit of any God, but must be wholly guided by chance and fortune. Whereas the government and providence of a certain definite number of worlds has nothing in it that seems more laborious and unworthy than that which is employed in the direction of one alone, which is transformed, renewed, and reformed an infinite number of times.
30. ἐκεῖνος δʼ οἶμαι σεμνότερος ὁ λόγος καὶ μεγαλοπρεπέστερος, ἀδεσπότους καὶ αὐτοκρατεῖς τοὺς θεοὺς ὄντας, ὥσπερ οἱ Τυνδαρίδαι τοῖς χειμαζομένοις βοηθοῦσινἐπερχόμενοί τε μαλάσσοντες βίᾳ τὸνπόντον ὠκείας τʼ ἀνέμων ῥιπάςοὐκ ἐμπλέοντες αὐτοὶ καὶ συγκινδυνεύοντες ἀλλʼ ἄνωθεν ἐπιφαινόμενοι καὶ σῴζοντες· οὕτως ἐπιέναι τῶν κόσμων ἄλλοτʼ ἄλλον, ἡδονῇ τε τῆς θέας ἀγομένους καὶ τῇ φύσει συναπευθύνοντας ἕκαστον. ὁ μὲν γὰρ Ὁμηρικὸς Ζεὺς οὐ πάνυ πρόσω μετέθηκε τὴν ὄψιν ἀπὸ Τροίας ἐπὶ τὰ Θρᾴκια καὶ τοὺς περὶ τὸν Ἴστρον νομάδας, ὁ δʼ ἀληθινὸς ἔχει καλὰς καὶ πρεπούσας ἐν πλείοσι κόσμοις μεταβολάς, οὐχὶ κενὸν ἄπειρον ἔξω βλέπων οὐδʼ ἑαυτὸν ἄλλο δʼ οὐδὲν ʽ ὡς ᾠήθησαν ἔνιοἰ νοῶν, ἀλλʼ ἔργα τε θεῶν καὶ ἀνθρώπων πολλὰ κινήσεις τε καὶ φορὰς ἄστρων ἐν περιόδοις καταθεώμενος. οὐ γὰρ ἀπεχθάνεται μεταβολαῖς ἀλλὰ καὶ πάνυ χαίρει τὸ θεῖον, εἰ δεῖ τῶν φαινομένων τεκμαίρεσθαι ταῖς κατʼ οὐρανὸν ἐξαμείψεσι καὶ περιόδοις. ἡ μὲν οὖν ἀπειρία παντάπασιν ἀγνώμων καὶ ἄλογος καὶ μηδαμῇ προσιεμένη θεόν, ἀλλὰ χρωμένη πρὸς πάντα τῷ κατὰ τύχην καὶ αὐτομάτως· ἡ δʼ ἐν ὡρισμένῳ πλήθει καὶ ἀριθμῷ κόσμων ἐπιμέλεια καὶ πρόνοια τῆς εἰς ἓν δεδυκυίας σῶμα καὶ προσηρτημένης ἑνὶ καὶ τοῦτο μετασχηματιζούσης καὶ ἀναπλαττούσης ἀπειράκις ἔμοιγε δοκεῖ μηδὲν ἔχειν ἀσεμνότερον μηδʼ ἐπιπονώτερον.
31. Having said this, I paused. And Philippus immediately cried out: Whether this be certain or not, I will not be too positive; but if we carry God beyond one world, it would more gratify me to know why we should make him the Creator only of five worlds and no more, and what proportion this number bears to that of the worlds, than to know why the word E I was inscribed upon this temple. For this is neither a triangular, a quadrate, a perfect, nor a cubic number, neither does it yield any elegancy to such as are delighted in this kind of sciences. As to what concerns the argument dawn from the number of elements, which Plato seems to have touched upon, it is obscure and improbable, and will not afford this consequence,—that, as there are formed from matter five sorts of regular bodies, which have equal angles and equal sides, and are environed with equal superficies, so there were from the beginning five worlds, made and formed of these five bodies.
31. ἐγὼ μὲν οὖν τοσαῦτʼ εἰπὼν ἐπέσχον. ὁ δὲ Φίλιππος οὐ πολὺν χρόνον διαλιπών τὸ μὲν ἀληθές ἔφη περὶ τούτων οὕτως ἔχειν ἢ ἑτέρως οὐκ ἂν ἔγωγε διισχυρισαίμην εἰ δὲ τὸν θεὸν ἐκβιβάζομεν ἑνὸς κόσμου, διὰ τί πέντε μόνων οὐ πλειόνων ποιοῦμεν δημιουργόν, καί τίς ἔστι τοῦ ἀριθμοῦ τούτου πρὸς τὸ πλῆθος λόγος, ἣδιον ἄν μοι δοκῶ μαθεῖν ἢ τῆς ἐνταῦθα τοῦ Ε καθιερώσεως τὴν διάνοιαν. οὔτε γὰρ τρίγωνος ἢ τετράγωνος οὔτε τέλειος ἢ κυβικὸς οὔτʼ ἄλλην τινὰ φαίνεται κομψότητα παρέχων τοῖς ἀγαπῶσι τὰ τοιαῦτα καὶ θαυμάζουσιν. ἡ δʼ ἀπὸ τῶν στοιχείων ἔφοδος, ἣν αὐτὸς ὑπῃνίξατο, πάντῃ δύσληπτός ἐστι καὶ μηδὲν ὑποφαίνουσα τῆς ἐκεῖνον ἐπεσπασμένης πιθανότητος εἰπεῖν, ὡς εἰκός ἐστι πέντε σωμάτων ἰσογωνίων καὶ ἰσοπλεύρων καὶ περιεχομένων ἴσοις ἐπιπέδοις, ἐγγενομένων τῇ ὕλῃ, τοσούτους εὐθὺς ἐξ αὐτῶν ἀποτελεσθῆναι κόσμους.
32. Yet Theodorus the Solian, said I, when he reads Plato’s mathematics to his scholars, both keeps to the text and clearly expounds it, when he saith, the pyramid, octahedron, dodecahedron. icosahedron (which Plato lays down as the first bodies) are all beautiful both in their proportions and equalities; Nature cannot contrive and make better than these, nor perhaps so good. Yet they have not all the same constitution and origin; for the least and slightest of the five is the pyramid; the greatest, which has most parts, is the dodecahedron; and of the other two, the icosahedron is greater than the octahedron by more than twofold, if you compare their number of triangles. And therefore it is impossible they should be all made at once, of one and the same matter; for the smallest and most subtile have been certainly more pliable to the hand of the workman who moved and fashioned the matter, and consequently were sooner made and shaped, than those which have stronger parts and a greater mass of bodies, and whose composition was more laborious and difficult, like the dodecahedron. Whence it follows that the pyramid was the first body, and not one of the others, which were by nature last produced. Now the way also to avoid this absurdity is to separate and divide matter into five worlds; here the pyramid (for she is the first and most simple), there the octahedron, and there the icosahedron; and out of that which exists first in every one of these the rest draw their original by the concretion of parts, by which every thing is changed into every thing, as Plato himself shows us by examples throughout. But it will suffice us briefly to learn thus much. Air is engendered by the extinction of fire, and the same being subtilized and rarefied produceth fire. Now by the seeds of these two we may find out the passions and transmutations of all. The seminary or beginning of fire is the pyramid, consisting of twenty-four first triangles; and the octahedron is the seminary of the air, consisting of forty-eight triangles of the same kind. So that the one element of air stands upon two of fire, joined together and condensed. And again, one body or element of air is divided into two of fire, which again, becoming thick and hard, is changed into water; so that, throughout, that which comes first into light gives easily birth unto the rest by transmutation. And so it comes to pass, that there is not merely one first principle of all things; but one thing is so mixed with the origin of another, in the several changes and alterations of nature by motion, that the same name and denomination belong equally to all.
32. καὶ μήνʼ ἔφην ἐγὼ δοκεῖ Θεόδωρος ὁ Σολεὺς οὐ φαύλως μετιέναι τὸν λόγον, ἐξηγούμενος τὰ μαθηματικὰ τοῦ Πλάτωνος. μέτεισι δʼ οὕτως. πυραμὶς καὶ ὀκτάεδρον καὶ εἰκοσάεδρον καὶ δωδεκάεδρον, ἃ πρῶτα τίθεται Πλάτων, καλὰ μέν ἐστι πάντα συμμετρίαις λόγων καὶ ἰσότησι, καὶ κρεῖσσον οὐδὲν αὐτῶν οὐδʼ ὅμοιον ἄλλο συνθεῖναι τῇ φύσει καὶ συναρμόσαι λέλειπται. μιᾶς γε μὴν πάντα συστάσεως οὐκ εἴληχεν οὐδʼ ὁμοίαν ἔχει τήν γένεσιν, ἀλλὰ λεπτότατον μέν ἐστι καὶ μικρότατον ἡ πυραμίς, μέγιστον δὲ καὶ πολυμερέστατον τὸ δωδεκάεδρον· τῶν δὲ λειπομένων δυεῖν τοῦ ὀκταέδρου μεῖζον ἢ διπλάσιον πλήθει τριγώνων τὸ εἰκοσάεδρον, διὸ τὴν γένεσιν ἅμα πάντα λαμβάνειν ἐκ τὴν ὕλης ἀδύνατόν ἐστι. τὰ γὰρ λεπτὰ καὶ μικρὰ καὶ ταῖς κατασκευαῖς ἁπλούστερα πρῶτα τῷ κινοῦντι καὶ διαπλάττοντι τὴν ὕλην ὑπακούειν ἀνάγκη καὶ συντελεῖσθαι καὶ προϋφίστασθαι τῶν ἁδρομερῶν καὶ πολυσωμάτων καὶ τὴν σύστασιν ἐργωδεστέραν ἐχόντων, ἐξ ὧν τὸ δωδεκάεδρον. ἕπεται δὲ τούτῳ τὸ μόνον εἶναι σῶμα πρῶτον τὴν πυραμίδα, τῶν δʼ ἄλλων μηδέν, ἀπολειπομένων τῇ φύσει τῆς γενέσεως. ἔστιν οὖν ἴαμα καὶ ταύτης τῆς ἀτοπίας ἡ τῆς ὕλης εἰς πέντε κόσμους διαίρεσις καὶ διάστασις. ὅπου μὲν γὰρ πυραμὶς ʽ ὑπέστησε γὰρ πρῶτον̓, ὅπου δʼ ὀκτάεδρον, ὅπου δʼ εἰκοσάεδρον. ἐκ δὲ τοῦ προϋποστάντος ἐν ἑκάστῳ τὰ λοιπὰ τὴν γένεσιν ἕξει, κατὰ σύγκρισιν καὶ διάκρισιν μερῶν εἰς πάντα γιγνομένης πᾶσι μεταβολῆς, ὡς αὐτὸς ὁ Πλάτων ὑποδείκνυσι διὰ πάντων σχεδὸν ἐπεξιών ἡμῖν δὲ βραχέως ἀρκέσει μαθεῖν. ἐπεὶ γὰρ ἀὴρ μὲν σβεννυμένου πυρὸς ὑφίσταται, καὶ λεπτυνόμενος αὖθις ἐξ αὑτοῦ πῦρ ἀναδίδωσιν, ἐν τοῖς ἑκατέροις σπέρμασι τὰ πάθη δεῖ θεᾶσθαι καὶ τὰς μεταβολάς. σπέρματα δὲ πυρὸς μὲν ἡ πυραμίς, ἐξ εἴκοσι καὶ τεσσάρων πρώτων τριγώνων· τὸ δʼ ὀκτάεδρον ἀέρος ἐκ τεσσαράκοντα καὶ ὀκτὼ τῶν αὐτῶν γίγνεται. γίγνεται τοίνυν ἀέρος μὲν ἓν στοιχεῖον, ἐκ δυεῖν πυρὸς … συγκραθέντων καὶ συστάντων, τὸ δʼ ἀέρος αὖ κερματιζόμενον εἰς δύο πυρὸς διακρίνεται σώματα, συνθλιβόμενον δʼ αὖθις αὑτῷ καὶ συμπῖπτον εἰς ὕδατος ἰδέαν ἄπεισιν. ὥστε πανταχοῦ τὸ προϋφιστάμενον ἀεὶ πᾶσι τοῖς ἄλλοις εὐπόρως παρέχειν τὴν γένεσιν ἐκ τῆς μεταβολῆς· καὶ μὴ μόνον ἓν εἶναι πρῶτον, ἑτέρου δʼ ἐν ἑτέρῳ συστήματι κίνησιν ἀρχηγὸν καὶ προληπτικὴν ἐς γένεσιν ἔχοντος πᾶσι τηρεῖσθαι τὴν ὁμωνυμίαν.
33. But here Ammonius interrupted him, and said: Notwithstanding that those things are so peremptorily and so pompously asserted by Theodorus, yet I shall wonder if he be not forced to make use of such suppositions as are destructive of themselves and one of another. For he will have it, that the five worlds he speaks of were not composed all at one time, but that that which was subtilest, and which gave least trouble in the making, came out first into being. And as if it were a consequent, and not a repugnant thing, he supposes that the matter does not always drive out into existence that which is most subtile and simple, but that sometimes the thickest, grossest, and heaviest parts do anticipate the more subtile in generation. But besides this, supposing that there be five primitive bodies or elements, and consequently that there be as many worlds, there are but four of those orders which he discourses rationally concerning. For as to the cube, he takes it away and removes it, as it were in a game of counters; for it is naturally unfit either to turn into any thing besides itself, or to yield that any of those other bodies be converted into it, inasmuch as the triangles of which they consist be not of the same sort. For all the rest consist in common of demi-triangles (or halves of equilateral triangles); but the proper subject of which the cube is particularly composed is the right isosceles triangle, which admits no inclination to a demi-triangle, nor can possibly be united and incorporated with it. If there be then five bodies, and consequently five worlds, and in each of these worlds the principle of generation be that body which is first produced, it must happen that, where the cube is the first in generation, none of the rest can possibly be produced, it being contrary to its nature to change into any of them. Not to insist here, that Theodorus and those of his mind make the element or principle of which the dodecahedron is composed to be different from the rest, it not being that triangle which is termed scalene, with three unequal sides, out of which the pyramid, octahedron, and icosahedron, according to Plato, are produced; so that (said Ammonius laughing) you must solve these objections, or offer something new concerning the matter in debate.
33. καὶ ὁ Ἀμμώνιος; ἀνδρικῶς μέν ἔφη ταῦτα τῷ Θεοδώρῳ καὶ φιλοτίμως διαπεπόνηται θαυμάσαιμι δʼ ἄν, εἰ μὴ δόξειε χρῆσθαι λήμμασιν ἀναιρετικοῖς ἀλλήλων. ἀξιοῖ γὰρ ἅμα πᾶσι τοῖς πέντε μὴ γίγνεσθαι τὴν σύστασιν, ἀλλὰ τὸ λεπτότατον ἀεὶ καὶ διʼ ἐλάττονος πραγματείας συνιστάμενον προεκπίπτειν εἰς γένεσιν. εἶθʼ ὥσπερ ἀκόλουθον οὐ μαχόμενον τούτῳ τίθησι τὸ μὴ πᾶσαν ὕλην πρῶτον εἰσφέρειν τὸ λεπτότατον καὶ ἁπλούστατον, ἀλλʼ ἐνιαχῆ τὰ ἐμβριθῆ καὶ πολυμερῆ φθάνειν προανίσχοντα ταῖς γενέσεσιν ἐκ τῆς ὕλης. ἄνευ δὲ τούτου, πέντε σωμάτων πρώτων ὑποκειμένων καὶ διὰ τοῦτο κόσμων λεγομένων εἶναι τοσούτων, πρὸς μόνα τὰ τέσσαρα τῇ πιθανότητι χρῆται, τὸν δὲ κύβον ὥσπερ ἐν παιδιᾷ ψήφων ὑφῄρηται, μήτʼ αὐτὸν εἰς ἐκεῖνα μεταβάλλειν πεφυκότα μήτʼ ἐκείνοις παρέχειν μεταβολὴν εἰς ἑαυτόν, ἅτε δὴ τῶν τριγώνων οὐχ ὁμογενῶν ὄντων. ἐκείνοις μὲν γὰρ ὑπόκειται κοινὸν ἐν πᾶσι τὸ ἡμιτρίγωνον, ἐν τούτῳ δʼ ἴδιον μόνῳ τὸ ἰσοσκελές, οὐ ποιοῦν πρὸς ἐκεῖνο σύννευσιν οὐδὲ σύγκρασιν ἑνωτικήν. εἴπερ οὖν πέντε σωμάτων ὄντων καὶ πέντε κόσμων, ἓν ἐν ἑκάστῳ τὴν ἡγεμονίαν ἔχει τῆς γενέσεως, ὅπου γέγονεν ὁ κύβος πρῶτος, οὐδὲν ἔσται τῶν ἄλλων εἰς οὐδὲν γὰρ ἐκείνων μεταβάλλειν πέφυκεν. ἐῶ γάρ, ὅτι καὶ τὸ τοῦ καλουμένου δωδεκαέδρου στοιχεῖον ἄλλο ποιοῦσιν, οὐκ ἐκεῖνο τὸ σκαληνόν, ἐξ οὗ τὴν πυραμίδα καὶ τὸ ὀκτάεδρον καὶ τὸ εἰκοσάεδρον ὁ Πλάτων συνίστησιν. ὥσθʼ ἅμα γελῶν ὁ Ἀμμώνιος εἶπεν ἢ ταῦτά σοι διαλυτέον ἢ ἴδιόν τι λεκτέον περὶ τῆς κοινῆς ἀπορίας.
34. And I answered him, that, for my part, I knew not at present how to say any thing which carried more probability. But perhaps (said I) it is better for a man to give an account of his own opinion than of another’s. Therefore I say that, there being supposed from the beginning of things two several natures contrary to each other,— the one sensible, mutable, subject to generation, corruption, and change every way, the other spiritual and intelligible, and abiding always in the same state,—it would be very strange, my friends, to say that the spiritual nature admitteth of division and hath diversity and difference in it, and to be angry if a man will not allow the passible and corporeal nature to be wholly united in itself, without dividing it into many parts. For it is most suitable to the permanent and divine natures to be tied and linked to each other, and to avoid, as much as is possible, all division and separation; and yet, amongst incorporeal natures the power of diversity works greater differences in regard to essential forms and reason, than those of distance of place in the corporeal world. And therefore Plato, refuting those who hold this proposition, that all is one, asserts these five grounds and principles of all,—entity, identity, diversity, motion, and rest; which five immaterial principles being admitted, it is no marvel if Nature have made every one of these to be an imitation, though not exact, yet as perfect and agreeable as could be drawn, of a correspondent principle in the corporeal mystery, partaking, as much as can be, of its power and virtue. For it is very plain that the cube is most proper and agreeable to repose and rest, by reason of the stability and firmness of those plain surfaces of which it consists. And as to the pyramid, everybody soon sees and acknowledges the nature of fire in it, by the slenderness of its decreasing sides, and the sharpness of its angles; and the nature of the dodecahedron, apt to comprehend all the other figures, may seem more properly to be the corporeal image of Ens, or Being in the general, indifferent to this or that particular form or shape. And of the other two which remain, the icosahedron resembleth the principle of diversity, and the octahedron principally partakes of the identical nature. And thus from one of these the air is produced, which partakes of and borders upon every substance, under one and the same outward form and appearance; and the other has afforded us the element of water, which by mixture may put on the greatest diversity of qualities. Therefore if Nature requires a certain uniformity and harmony in all things, it must be then that there are neither more nor fewer worlds in the corporeal nature than there are patterns or samples in the incorporeal, to the end that each pattern or sample in the invisible nature may have its own primary position and power, answering to a secondary or derivative in the different constitution or composition of bodies.
34. κἀγώ πιθανώτερον οὐδὲν ἔχω λέγειν ἔν γε τῷ παρόντι· βέλτιον δʼ ἴσως ἐστὶν ἰδίας εὐθύνας ὑπέχειν δόξης ἢ ἀλλοτρίας;. λέγω τοίνυν αὖθις ἐξ ἀρχῆς, ὅτι δυεῖν ὑποκειμένων φύσεων, τῆς μὲν αἰσθητῆς ἐν γενέσει καὶ φθορᾷ μεταβόλου καὶ φορητῆς ἄλλοτʼ ἄλλως, ἑτέρας δʼ ἐν οὐσίᾳ νοητῆς ἀεὶ κατὰ ταὐτὰ ὡσαύτως ἐχούσης, δεινόν ἐστιν, ὦ ἑταῖρε, τὴν μὲν νοητὴν διωρίσθαι καὶ διαφορὰν ἔχειν ἐν ἑαυτῇ, τὴν δὲ σωματικὴν καὶ παθητικὴν εἰ μὴ μίαν τις ἀπολείπει συμπεφυκυῖαν αὑτῇ καὶ συννεύουσαν ἀλλὰ χωρίζει καὶ διίστησιν, ἀγανακτεῖν καὶ δυσχεραίνειν. τὰ γὰρ μόνιμα καὶ θεῖα δήπου μᾶλλον αὑτῶν ἔχεσθαι προσήκει καὶ φεύγειν ὡς ἀνυστόν ἐστι τομὴν ἅπασαν καὶ διάστασιν. ἀλλὰ καὶ τούτων ἡ τοῦ ἑτέρου δύναμις ἁπτομένη μείζονας ἐνείργασται τῶν κατὰ τόπον διαστάσεων τοῖς νοητοῖς τὰς κατὰ λόγον καὶ ἰδέαν ἀνομοιότητας. ὅθεν ἐνιστάμενος τοῖς ἓν τὸ πᾶν ἀποφαίνουσιν ὁ Πλάτων, τὸ τʼ ὂν εἶναί φησι καὶ τὸ ταὐτὸν καὶ τὸ ἕτερον, ἐπὶ πᾶσι δὲ κίνησιν καὶ στάσιν. ὄντων οὖν πέντε τούτων, οὐ θαυμαστὸν ἦν, εἰ τῶν πέντε σωματικῶν στοιχείων ἐκείνων ἕκαστον ἑκάστου μίμημα τῇ φύσει; καὶ εἴδωλόν ἐστι γεγενημένον οὐκ ἄμικτον οὐδʼ εἰλικρινές, ἀλλὰ τῷ μάλιστα μετέχειν ἕκαστον ἑκάστης δυνάμεως. ὁ μέν γε κύβος ἐμφανῶς στάσεως οἰκεῖόν ἐστι σῶμα διὰ τὴν τῶν ἐπιπέδων ἀσφάλειαν καὶ βεβαιότητα· τῆς δὲ πυραμίδος πᾶς ἄν τις τὸ πυροειδὲς καὶ κινητικὸν ἐν τῇ λεπτότητι τῶν πλευρῶν καὶ τῇ τῶν γωνιῶν ὀξύτητι κατανοήσειεν· ἡ δὲ τοῦ δωδεκαέδρου φύσις, περιληπτικὴ τῶν ἄλλων σχημάτων οὖσα τοῦ ὄντος εἰκὼν πρὸς πᾶν ἂν τὸ σωματικὸν γεγονέναι δόξειε· τῶν δὲ λοιπῶν δυεῖν τὸ μὲν εἰκοσάεδρον τῆς τοῦ ἑτέρου τὸ δʼ ὀκτάεδρον μάλιστα τῆς ταὐτοῦ μετείληχεν ἰδέας. διὸ τοῦτο μὲν ἀέρα σχετικὸν οὐσίας πάσης ἐν μιᾷ μορφῇ, θάτερον δʼ ὕδωρ ἐπὶ πλεῖστα τῷ κεράννυσθαι γένη ποιοτήτων τρεπόμενον παρεῖχεν. εἴπερ οὖν ἡ φύσις ἀπαιτεῖ τὴν ἰσονομίαν ἐν πᾶσι, καὶ κόσμους εἰκός ἐστι μήτε πλείους γεγονέναι μήτʼ ἐλάττους τῶν παραδειγμάτων, ὅπως ἕκαστον ἐν ἑκάστῳ τάξιν ἡγεμονικὴν ἔχῃ καὶ δύναμιν, ὥσπερ ἐν ταῖς συστάσεσι τῶν σωμάτων ἔσχηκεν.
35. And this may serve for an answer to those that wonder at our dividing Nature, subject to generation and alteration, into so many kinds. But I entreat you all further, attentively to consider with yourselves that, of the two first and supreme principles of all things,—that is to say, the unity, and the indefinite binary or duality,—this latter, being the element and chief origin of all deformity and disorder, is termed infinity, and on the contrary, the nature of unity, determining and limiting the void infinity, which has no proportion nor termination, reduces it into form, and renders it in some manner capable of receiving a denomination which belongs only to sensible and particular things. Now these two general principles appear first in number; for the multitude is indeed no number, unless a certain form of the matter resulting out of indeterminate infinity is cut off, and bounded within respective limits, either shorter or longer. For then each multitude is made number, when once it is determined and limited by unity; whereas, if we take away unity, then the indeterminate duality brings all into confusion, and renders it without harmony, without number or measure. Now, the form not being the destruction of matter, but rather the order and the beauty of it, both these principles therefore must be within number, from whence ariseth the chief disparity and greatest difference. For the infinite and indeterminate principle is the cause of the even number; and the other better principle, which is the unity, is the father (as it were) of the odd number. So that the first even number is two, and the first odd number is three; of which is composed five by conjunction, which is by its composition common to both, but of power or nature not even but odd. For, since sensible and corporeal nature is divided into several parts, on account of its inborn necessity of diversity, it was necessary that the number of these parts should not be either the first even number, nor yet the first uneven or odd, but a third, consisting of both; to the end that it might be procreated out of both principles, viz. of that which causeth the even number, and of that which produceth the odd; for the one cannot be parted from the other, inasmuch as both have the nature, power, and force of a principle. These two principles being then joined together, the better one being mightier prevails over the indeterminate infinity or duality, which divideth the corporeal nature; and thus the matter being divided, the unity interposing itself between has hindered the universe from being divided and parted into two equal portions. But there has been a multitude of worlds caused by the diversity and disagreement of the infinite Nature; but this multitude was brought into an odd number by the virtue and power of identity, or the finite principle; and it was therefore odd, because the better principle would not suffer Nature to stretch itself further than was fitting. For if there had been nothing but pure and simple unity, the matter would have known no separation; but being mixed with the dividing nature of duality, it has by this means suffered separation and division; yet it has stopped here, by the odd numbers being the superior and master to the even.
35. οὐ μὴν ἀλλὰ τοῦτο μὲν ἔστω παραμυθία τοῦ θαυμάζοντος, εἰ τὴν ἐν γενέσει καὶ μεταβολῇ φύσιν εἰς γένη τοσαῦτα διαιροῦμεν. ἐκεῖνο δʼ ἤδη σκοπεῖτε κοινῇ προσέχοντες, ὅτι τῶν ἀνωτάτω ἀρχῶν, λέγω δὲ τοῦ ἑνὸς καὶ τῆς ἀορίστου δυάδος, ἡ μὲν ἀμορφίας πάσης στοιχεῖον οὖσα καὶ ἀταξίας ἀπειρία κέκληται ἡ δʼ τοῦ ἑνὸς φύσις ὁρίζουσα καὶ καταλαμβάνουσα τῆς ἀπειρίας τὸ κενὸν καὶ ἄλογον καὶ ἀόριστον ἔμμορφον παρέχεται, καὶ τὴν ἑπομένην περὶ τὰ αἰσθητὰ δείξει καταγόρευσιν ἁμωσγέπως ὑπομένον καὶ δεχόμενον. αὗται δὲ πρῶτον αἱ ἀρχαὶ περὶ τὸν ἀριθμὸν ἐπιφαίνονται, μᾶλλον δʼ ὅλως ἀριθμὸς οὐκ ἔστι τὸ πλῆθος, ἂν μὴ καθάπερ εἶδος ὕλης τὸ ἓν γενόμενον ἐκ τῆς ἀπειρίας τοῦ ἀορίστου πῆ μὲν πλεῖον πῆ δʼ ἔλαττον ἀποτέμνηται. τότε γὰρ ἀριθμὸς γίγνεται τῶν πληθῶν ἕκαστον ὑπὸ τοῦ ἑνὸς ὁριζόμενον ἐὰν δʼ ἀναιρεθῇ τὸ ἕν, πάλιν ἡ ἀόριστος δυὰς συγχέασα πᾶν ἄρρυθμον καὶ ἄπειρον καὶ ἄμετρον ἐποίησεν. ἐπεὶ δὲ τὸ εἶδος οὐκ ἀναίρεσίς ἐστι τῆς ὕλης ἀλλὰ μορφὴ καὶ τάξις ὑποκειμένης, ἀνάγκη καὶ τῷ ἀριθμῷ τὰς ἀρχὰς ἐνυπάρχειν ἀμφοτέρας, ὅθεν ἡ πρώτη καὶ μεγίστη διαφορὰ καὶ ἀνομοιότης γέγονεν. ἔστι γὰρ ἡ μὲν ἀόριστος ἀρχὴ τοῦ ἀρτίου δημιουργὸς ἡ δὲ βελτίων τοῦ περιττοῦ πρῶτος δὲ τῶν ἀρτίων τὰ δύο καὶ τὰ τρία τῶν περιττῶν, ἐξ ὧν τὰ πέντε τῇ μὲν συνθέσει κοινὸς ὢν ἀμφοῖν ἀριθμὸς τῇ δὲ δυνάμει γεγονὼς περιττός. ἔδει γάρ, εἰς πλείονα μέρη τοῦ αἰσθητοῦ καὶ σωματικοῦ μεριζομένου διὰ τὴν σύμφυτον ἀνάγκην τῆς ἑτερότητος, μήτε τὸν πρῶτον ἄρτιον γενέσθαι μήτε τὸν πρῶτον περιττόν, ἀλλὰ τὸν τρίτον ἐκ τούτων ἀποτελούμενον, ὅπως ἀπʼ ἀμφοτέρων τῶν ἀρχῶν γένηται, καὶ τῆς τὸ ἄρτιον δημιουργούσης καὶ τῆς τὸ περιττόν· οὐ γὰρ ἦν οἷόν τε τῆς ἑτέρας ἀπαλλαγῆναι τὴν ἑτέραν· ἑκατέρα γὰρ ἀρχῆς; φύσιν ἔχει καὶ δύναμιν. ἀμφοτέρων οὖν συνδυαζομένων, ἡ βελτίων κρατήσασα τῆς ἀοριστίας διαιρούσης τὸ σωματικὸν ἐνέστη, καὶ τῆς ὕλης ἐν ἀμφοτέροις διισταμένης μέσην τὴν μονάδα θεμένη δίχα νεμηθῆναι τὸ πᾶν οὐκ εἴασεν, ἀλλὰ πλῆθος μὲν γέγονε κόσμων ὑπὸ τῆς ἑτερότητος τοῦ ἀορίστου καὶ διαφορᾶς, περιττὸν δὲ πλῆθος ἡ ταὐτοῦ καὶ ὡρισμένου δύναμις ἀπείργασται, περιττὸν δὲ τοιοῦτον, ὅτι πορρωτέρω τὴν φύσιν ἢ βέλτιον ἔχει προελθεῖν οὐκ εἴασεν. εἰ μὲν γὰρ ἀμιγὲς καὶ καθαρὸν ἦν τὸ ἕν, οὐδʼ ἂν ὅλως εἶχεν ἡ ὕλη διάστασιν· ἐπεὶ δὲ τῷ διαιρετικῷ τῆς δυάδος μέμικται, τομὴν μὲν ἐδέξατο καὶ διαίρεσιν, ἐνταῦθα δʼ ἔστη τῷ περισσῷ τοῦ ἀρτίου κρατηθέντος.
36. This is the reason why the ancients were used to express numbering or reckoning by πεμπάσασθαι, to count by fives. And I am of opinion that that word πάντα, all, is derived from πέντε, which is to say five, five being compounded of the first numbers. For all the other numbers being afterwards multiplied by others, they produce numbers different from themselves; whereas five, being multiplied by an even number, produceth a perfect ten, and multiplied by an odd number, representeth itself again; not to insist that it is composed of the two first tetragons or quadrate numbers (unity and four), and that, being the first number whose square is equivalent to the two squares before it, it composeth the fairest of right angled triangles, and is the first number which containeth the sesquilateral proportion. Perhaps all these reasons are not very pertinent to the discourse of the present dispute, it being better to allege that in this number there is a natural virtue of dividing, and that nature divideth many things by this number. For in ourselves she has placed five senses, and five parts of the soul, the vital, the sensitive, the concupiscible, the irascible, and the rational; and as many fingers on each hand; and the most fruitful seed disperseth itself but into five, for we read nowhere of a woman that brought forth more than five at a birth. And the Egyptians also tell us that the Goddess Rhea was delivered of five Gods, giving us to understand in covert terms that of the same matter were procreated five worlds. And in the universe, the earth is divided into five zones, the heaven into five circles,—two arctics, two tropics, and one equinoctial in the midst. There are five revolutions of planets or wandering stars, inasmuch as the Sun, Venus, and Mercury make but one and the same revolution. And the construction of the world consists of an harmonical measure; even as our musical chords consist of the posture of five tetrachords, ranged orderly one after another, that is to say, those called ὑπάτων, μέσων, συνημμένων, διεζευγμένων, and ὑπερβολαίων. The intervals also which are used in singing are five, diesis, semitone, tone, the tone and a half, and the double tone; so that Nature seems to delight more in making all things according to the number five, than she does in producing them in a spherical form, as Aristotle writeth.
36. διὸ καὶ πεμπάσασθαι τὸ ἀριθμῆσαι τοῖς παλαιοῖς ἔθος ἦν καλεῖν. οἶμαι δὲ καὶ τὰ πάντα τῶν πέντε παρώνυμα γεγονέναι κατὰ λόγον, ἅτε δὴ τῆς πεντάδος ἐκ τῶν πρώτων ἀριθμῶν συνεστώσης. καὶ γὰρ οἱ μὲν ἄλλοι πολλαπλασιαζόμενοι πρὸς ἄλλους εἰς ἕτερον αὑτῶν ἀριθμὸν ἐκβαίνουσιν ἡ δὲ πεντάς, ἂν μὲν ἀρτιάκις λαμβάνηται, τὸν δέκα ποιεῖ τέλειον· ἐὰν δὲ περισσάκις, ἑαυτὴν πάλιν ἀποδίδωσιν. ἐῶ δʼ ὅτι πρώτη μὲν ἐκ πρώτων δυεῖν τετραγώνων συνέστηκε τῆς τε μονάδος καὶ τῆς τετράδος ἡ πεντάς, πρώτη δʼ ἴσον δυναμένη τοῖς πρὸ αὑτῆς δυσὶ τὸ κάλλιστον τῶν ὀρθογωνίων τριγώνων συνίστησι πρώτη δὲ ποιεῖ τὸν ἡμιόλιον λόγον. οὐ γὰρ ἴσως οἰκεῖα ταῦτα τοῖς ὑποκειμένοις πράγμασιν· ἀλλʼ ἐκεῖνο μᾶλλον, τὸ φύσει διαιρετικὸν τοῦ ἀριθμοῦ καὶ τὸ πλεῖστα τούτῳ τὴν φύσιν διανέμειν. ἔνειμε γὰρ ἡμῖν αὐτοῖς αἰσθήσεις πέντε καὶ μέρη ψυχῆς, φυτικὸν ω· φυσικὸναἰσθητικὸν ἐπιθυμητικὸν θυμοειδὲς λογιστικόν· καὶ δακτύλους ἑκατέρας χειρὸς τοσούτους, καὶ τὸ γονιμώτατον σπέρμα πενταχῆ σχιζόμενον. οὐ γὰρ ἱστόρηται γυνὴ πλείονα τεκοῦσʼ ἢ πέντε τέκνα ταῖς αὐταῖς ὠδῖσι. καὶ τὴν Ῥέαν Αἰγύπτιοι μυθολογοῦσι πέντε θεοὺς τεκεῖν, αἰνιττόμενοι τὴν ἐκ μιᾶς ὕλης τῶν πέντε κόσμων γένεσιν. ἐν δὲ τῷ παντὶ πέντε μὲν ζώναις ὁ περὶ γῆν τόπος, πέντε δὲ κύκλοις ὁ οὐρανὸς διώρισται, δυσὶν ἀρκτικοῖς καὶ δυσὶ τροπικοῖς καὶ μέσῳ τῷ ἰσημερινῷ· πέντε δʼ αἱ τῶν πλανωμένων ἄστρων περίοδοι γεγόνασιν, ἡλίου καὶ Φωσφόρου καὶ στίλβοντος ὁμοδρομούντων. ἐναρμόνιος δὲ καὶ ἡ τοῦ κόσμου σύνταξις, ὥσπερ ἀμέλει καὶ τὸ παρʼ ἡμῖν ἡρμοσμένον ἐν πέντε τετραχόρδων θέσεσιν ὁρᾶται, τῶν ὑπάτων καὶ μέσων καὶ συνημμένων καὶ διεζευγμένων καὶ ὑπερβολαίων· καὶ τὰ μελῳδούμενα διαστήματα πέντε, δίεσις καὶ ἡμιτόνιον καὶ τόνος καὶ τριημιτόνιον καὶ δίτονον. οὕτως ἡ φύσις ἔοικε τῷ πέντε ποιεῖν ἅπαντα χαίρειν μᾶλλον ἢ τῷ σφαιροειδῆ, καθάπερ Ἀριστοτέλης ἔλεγε.
37. But it will perhaps be demanded, why Plato refers the number of worlds to the five regular bodies or figures, saying that God made use of the number five in the fabric of the world, as it were transcribing and copying this; and then, having proposed a doubt and question of the number of the worlds, whether there be five, or one only, thereby clearly shows that his conjecture is grounded on this conceit of the five regular bodies. If now we may make a probable conjecture as to his opinion, we may believe that of necessity, with the diversity of these figures and bodies, there must presently ensue a difference and diversity of motions; as he himself teacheth, affirming that whatever is subtilized or condensed does, at the same time with its alteration of substance, alter and change its place. For if from the air there is engendered fire, when the octahedron is dissolved and vanished into pyramids, or, on the contrary, if the air be produced from the fire pressed and squeezed up into the form of the octahedron, it is not possible it should remain there where it was before, but it flies and runs to another place, forcing and combating whatever stands in the way to oppose it. And he shows this more clearly and evidently by an example and similitude of fans, and such like things as drive away the chaff from the corn; for thus the elements driving the matter, and being driven by it, do always bring like to like, some taking up this place, others that, before the world was digested as now it is. The matter then being in that condition in which it is likely every thing is where God is not present, the five first qualities, or first bodies, having each their proper and peculiar inclinations and motions, went apart, not wholly and altogether, nor throughly divided and separated one from another; for when all was huddled in confusion, such as were surmounted went continually against their nature with the mightier. And therefore, some going on one side and others going on the other, hence it has happened that there have been as many portions and distinctions as there are divers kinds of first bodies; one of fire, not wholly pure, but inclining towards the form of fire; another of an ethereal nature, yet not wholly so, but inclining thereto; another of earth, not simple and mere earth, but inclining to the form of earth. But especially there was a communication of water and air; for these, as we have already mentioned, went their ways, replenished with divers other kinds. For God did not separate and distribute the matter, but having found it thus carelessly dissipated in itself, and each part being carried away in such great disorder and confusion, he ranged and ordered it into symmetry and proportion; and setting reason over each as a guardian and governor, he made as many worlds as there were first bodies. However, in respect to Ammonius, let these Platonical notions pass for what they are worth. For my part, I will never be overzealous in this precise number of worlds; but this I will say, that those who hold there are more than one, yet not an infinite number, have as good grounds as others, seeing the matter does naturally spread itself and is diffused into many parts,—not resting in one, while yet it is contrary to reason that it should be infinitely extended. In short, let us here especially be mindful of the wise precepts of the Academy, and preserve ourselves upon such slippery ground as the controversy concerning the infinity of worlds, by refusing a too confident assent.
37. τί δῆτα, φήσαι τις ἄν, ὁ Πλάτων ἐπὶ τὰ πέντε σχήματα τὸν τῶν πέντε κόσμων ἀριθμὸν ἀνήνεγκεν, εἰπὼν ὅτι τῇ πέμπτῃ συστάσει ὁ θεὸς ἐπὶ τὸ πᾶν κατεχρήσατο ἐκεῖνο διαζωγραφῶν· εἶτα τὴν περὶ τοῦ πλήθους τῶν κόσμων ὑποθεὶς ἀπορίαν, πότερον ἕνʼ ἢ πέντʼ αὐτοὺς ἀληθείᾳ πεφυκότας λέγειν προσήκει, δῆλός ἐστιν ἐντεῦθεν οἰόμενος ὡρμῆσθαι τὴν ὑπόνοιαν. εἴπερ οὖν δεῖ πρὸς τὴν ἐκείνου διάνοιαν ἐπάγειν τὸ εἰκός, σκοπῶμεν ὅτι ταῖς τῶν σωμάτων καὶ σχημάτων ἐκείνων διαφοραῖς ἀνάγκη καὶ κινήσεων εὐθὺς ἕπεσθαι διαφοράς, ὥσπερ αὐτὸς διδάσκει, τὸ διακρινόμενον ἢ συγκρινόμενον ἅμα τῆς οὐσίας τῇ ἑτεροιώσει καὶ τὸν τόπον μεταλλάττειν ἀποφαινόμενος. ἂν γὰρ ἐξ ἀέρος πῦρ γένηται, λυθέντος τοῦ ὀκταέδρου καὶ κερματισθέντος εἰς πυραμίδας, ἢ πάλιν ἀὴρ ἐκ πυρός, συνωσθέντος καὶ συνθλιβέντος εἰς ὀκτάεδρον, οὐ δυνατὸν μένειν ὅπου πρότερον ἦν, ἀλλὰ φεύγει καὶ φέρεται πρὸς ἑτέραν χώραν ἐκβιαζόμενον καὶ μαχόμενον τοῖς ἐνισταμένοις καὶ κατεπείγουσιν. ἔτι δὲ μᾶλλον εἰκόνι τὸ συμβαῖνον ἐνδείκνυται, τοῖς ὑπὸ τῶν πλοκάνων καὶ ὀργάνων τῶν περὶ τὴν τοῦ σίτου κάθαρσιν σειομένοις καὶ ἀναλικμωμένοις ὁμοίως λέγων τὰ στοιχεῖα σείοντα τὴν ὕλην ὑπʼ ἐκείνης; τε σειόμενα, προσχωρεῖν ἀεὶ τὰ ὅμοια τοῖς ὁμοίοις, ἄλλην τε χώραν ἄλλα ἴσχειν πρὶν ἐξ αὐτῶν γενέσθαι τὸ πᾶν διακοσμηθέν οὕτως οὖν τῆς ὕλης ἐχούσης ὡς ἔχειν τὸ πᾶν εἰκός, οὗ θεὸς ἄπεστιν, εὐθὺς αἱ πρῶται πέντε ποιότητες ἰδίας ἔχουσαι ῥοπὰς ἐφέροντο χωρίς, οὐ παντάπασιν οὐδʼ εἰλικρινῶς ἀποκρινόμεναι, διὰ τὸ πάντων ἀναμεμιγμένων ἀεὶ τὰ κρατούμενα τοῖς ἐπικρατοῦσι παρὰ φύσιν ἕπεσθαι. διὸ δὴ τοῖς τῶν σωμάτων γένεσιν ἄλλων ἀλλαχῆ φερομένων ἰσαρίθμους μερίδας καὶ διαστάσεις ἐποίησαν, τὴν μὲν οὐ καθαροῦ πυρὸς ἀλλὰ πυροειδῆ, τὴν δʼ οὐκ ἀμιγοῦς αἰθέρος ἀλλʼ αἰθεροειδῆ, τὴν δʼ οὐ γῆς αὐτῆς καθʼ ἑαυτὴν ἀλλὰ γεοειδῆ· μάλιστα δὲ καὶ τὴν ἀέρος κοίνωσιν τὴν ὕδατος διὰ τὸ πολλῶν, ὥσπερ εἴρηται, τῶν ἄλλων φύλων ἀναπεπλησμένʼ ἀπελθεῖν. οὐ γὰρ ὁ θεὸς διέστησεν οὐδὲ διῴκισε τὴν οὐσίαν, ἀλλʼ ὑπʼ αὐτῆς διεστῶσαν αὐτὴν καὶ φερομένην χωρὶς ἐν ἀκοσμίαις τοσαύταις παραλαβὼν, ἔταξε καὶ συνήρμοσε διʼ ἀναλογίας καὶ μεσότητος· εἶθʼ ἑκάστῃ λόγον ἐγκαταστήσας ὥσπερ ἁρμοστὴν καὶ φύλακα, κόσμους ἐποίησε τοσούτους, ὅσα γένη τῶν πρώτων σωμάτων ὑπῆρχε. ταῦτα μὲν οὖν τῇ Πλάτωνος ἀνακείσθω χάριτι διʼ Ἀμμώνιον· ἐγὼ δὲ περὶ μὲν ἀριθμοῦ κόσμων οὐκ ἄν ποτε διισχυρισαίμην ὅτι τοσοῦτοι, τὴν, δὲ πλείονας μὲν ἑνὸς οὐ μὴν ἀπείρους ἀλλʼ ὡρισμένους πλήθει τιθεμένην δόξαν, οὐδετέρας ἐκείνων ἀλογωτέραν ἡγοῦμαι, τὸ φύσει τῆς ὕλης σκεδαστὸν καὶ μεριστὸν ὁρῶν οὔτʼ ἐφʼ ἑνὸς μένον οὔτʼ εἰς ἄπειρον ὑπὸ τοῦ λόγου βαδίζειν ἐώμενον. εἰ δʼ ἀλλαχόθι που κἀνταῦθα τῆς Ἀκαδημείας ὑπομιμνήσκοντες ἑαυτοὺς τὸ ἄγαν τῆς πίστεως ἀφαιρῶμεν, καὶ τὴν ἀσφάλειαν ὥσπερ ἐν χωρίῳ σφαλερῷ, τῷ περὶ τῆς ἀπειρίας λόγῳ, μόνον διασῴζωμεν.
38. And when I had finished this discourse, Demetrius said: Lamprias is very much in the right; for the Gods deceive us with multiplicities, not of shadows and impostures (as Euripides expresseth it), but even of realities and substances themselves, when we presume to be positive, as if we understood them in things of such weight and moment. But we must, as he advises us, return to our first question, which we seem to have forgotten. For what was said concerning the oracles remaining dumb and useless when the Daemons who presided over them were departed, even as we see musical instruments yield no harmony when the musician does not handle them,—this, I say, brings a greater question into debate, namely touching the cause and power by which these Daemons use to make their prophets and prophetesses to be ravished with enthusiasm and filled with fantastical imaginations. For to say the oracles are silent as being forsaken by the Daemons is nothing, unless we be first shown how (when they are present and govern them) they set them at work and make them prophesy. Ammonius then taking up the discourse, Do you think, said he, that the Daemons are any thing else “Than wandering spirits clothed in finest air,” as Hesiod says? For as to my part, I think the same difference which there is between one man and another, when they act in a tragedy or comedy, is also to be found in this life in souls that are clothed with bodies. So that there is nothing in this which is strange or contrary to reason, if souls meeting with other souls do imprint on them visions and apprehensions of future things, just as we show several things already done and come to pass, and prognosticate of those which have not yet happened, not only by the help of speech, but also by letters and writings, or by a bare touch, or a single look;—unless you, Lamprias, are of another opinion. For we heard but very lately, that you discoursed at large upon this subject with the strangers that came to Lebadea; but he that gave us this information could give us no particular account of what passed. No wonder, replied I, for several avocations and businesses intervening, occasioned by the oracle and the solemn sacrifice that was then performing, made our discourse very broken and interrupted. But now, says Ammonius, you have auditors at leisure, that are inquisitive and desirous of instruction, so that you may speak freely, and expect all the candor and consideration which you can desire.
38. ἐμοῦ δὲ ταῦτʼ εἰπόντος, ὁ Δημήτριος ὀρθῶς ἔφη Λαμπρίας παραινεῖ. πολλαῖς γὰρ οἱ θεοὶ μορφαῖς οὐ σοφισμάτων ὡς Εὐριπίδης φησίν, ἀλλὰ πραγμάτων σφάλλουσιν ἡμᾶς, ὅταν ὡς ἐπιστάμενοι τολμῶμεν ἀποφαίνεσθαι περὶ τηλικούτων. ἀλλʼ ἀνοιστέος ὁ λόγος, ὡς ὁ αὐτὸς ἀνήρ φησιν, ἐπὶ τὴν ἐξ ἀρχῆς ὑπόθεσιν. τὸ γὰρ ἀφισταμένων καὶ ἀπολειπόντων τὰ χρηστήρια τῶν δαιμόνων ὥσπερ ὄργανα τεχνιτῶν ἀργὰ καὶ ἄναυδα κεῖσθαι λεχθέν, ἕτερον λόγον ἐγείρει τὸν περὶ τῆς αἰτίας μείζονα καὶ δυνάμεως, ᾗ χρώμενοι ποιοῦσι κατόχους τοῖς ἐνθουσιασμοῖς καὶ φαντασιαστικοὺς τοὺς προφήτας καὶ τὰς προφήτιδας. οὐ γὰρ οἷόν τε τὴν ἔκλειψιν αἰτιᾶσθαι τοῦ ἀπαυδᾶν τὰ μαντεῖα, μὴ πεισθέντας ὃν τρόπον ἐφεστῶτες αὐτοῖς καὶ παρόντες ἐνεργὰ καὶ λόγια ποιοῦσιν οἱ δαίμονες. ὑπολαβὼν δʼ ὁ Ἀμμώνιος οἴει γὰρ ἕτερόν τι τοὺς δαίμονας εἶπεν ἢ ψυχὰς ὄντας περιπολεῖν καθʼ Ἡσίοδον ἠέρα ἑσσαμένους;ʼ ἐμοὶ μὲν γάρ, ἣν ἄνθρωπος ἔχει διαφορὰν πρὸς ἄνθρωπον ὑποκρινόμενον τραγῳδίαν ἢ κωμῳδίαν, ταύτην ἔχειν δοκεῖ ψυχὴ πρὸς ψυχὴν ἐνεσκευασμένην σῶμα τῷ παρόντι βίῳ πρόσφορον. οὐδὲν οὖν ἄλογον οὐδὲ θαυμαστόν, εἰ ψυχαὶ ψυχαῖς ἐντυγχάνουσαι φαντασίας ἐμποιοῦσι τοῦ μέλλοντος, ὥσπερ ἡμεῖς ἀλλήλοις οὐ πάντα διὰ φωνῆς ἀλλὰ καὶ γράμμασι καὶ θιγόντες μόνον καὶ προσβλέψαντες πολλὰ καὶ μηνύομεν τῶν γεγονότων καὶ τῶν ἐσομένων προσημαίνομεν. εἰ μή τι σὺ λέγεις ἕτερον, ὦ Λαμπρία· καὶ γὰρ ἔναγχος ἧκέ τις φωνὴ πρὸς ἡμᾶς, ὡς σοῦ πολλὰ περὶ τούτων ἐν Λεβαδείᾳ ξένοις διαλεχθέντος, ὧν οὐδὲν ὁ διηγούμενος ἀκριβῶς διεμνημόνευσε. μὴ θαυμάσῃς ἔφην ἐγώ, πολλαὶ γὰρ ἅμα πράξεις διὰ μέσου καὶ ἀσχολίαι συντυγχάνουσαι διὰ τὸ μαντεῖον εἶναι καὶ θυσίαν, τοὺς λόγους διεσπαρμένους ἡμῖν καὶ σποράδας ἐποίησαν ἀλλὰ νῦν ὁ Ἀμμώνιος ἔφη καὶ σχολὴν ἄγοντας ἀκροατὰς ἔχεις καὶ προθύμους τὰ μὲν ζητεῖν τὰ δὲ μανθάνειν, ἔριδος ἐκποδὼν οὔσης καὶ φιλονεικίας ἁπάσης. συγγνώμης δὲ παντὶ λόγῳ καὶ παρρησίας ὡς ὁρᾷς δεδομένης.