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.
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.
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.
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.
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.
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.
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.
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.
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