51e. Now these two Kinds must be declared to be two, because they have come into existence separately and are unlike in condition. For the one of them arises in us by teaching, the other by persuasion; and the one is always in company with true reasoning, whereas the other is irrational; and the one is immovable by persuasion, whereas the other is alterable by persuasion; and of the one we must assert that every man partakes, but of Reason only the gods and but a small class of men.
51e. δύο δὴ λεκτέον ἐκείνω, διότι χωρὶς γεγόνατον ἀνομοίως τε ἔχετον. τὸ μὲν γὰρ αὐτῶν διὰ διδαχῆς, τὸ δʼ ὑπὸ πειθοῦς ἡμῖν ἐγγίγνεται· καὶ τὸ μὲν ἀεὶ μετʼ ἀληθοῦς λόγου, τὸ δὲ ἄλογον· καὶ τὸ μὲν ἀκίνητον πειθοῖ, τὸ δὲ μεταπειστόν· καὶ τοῦ μὲν πάντα ἄνδρα μετέχειν φατέον, νοῦ δὲ θεούς, ἀνθρώπων δὲ γένος βραχύ τι.
52. Tim. This being so, we must agree that One Kind is the self-identical Form, ungenerated and indestructible, neither receiving into itself any other from any quarter nor itself passing anywhither into another, invisible and in all ways imperceptible by sense, it being the object which it is the province of Reason to contemplate; and a second Kind is that which is named after the former and similar thereto, an object perceptible by sense, generated, ever carried about, becoming in a place and out of it again perishing, apprehensible by Opinion with the aid of Sensation; and a third Kind is ever-existing Place,
52. ΤΙ. τούτων δὲ οὕτως ἐχόντων ὁμολογητέον ἓν μὲν εἶναι τὸ κατὰ ταὐτὰ εἶδος ἔχον, ἀγέννητον καὶ ἀνώλεθρον, οὔτε εἰς ἑαυτὸ εἰσδεχόμενον ἄλλο ἄλλοθεν οὔτε αὐτὸ εἰς ἄλλο ποι ἰόν, ἀόρατον δὲ καὶ ἄλλως ἀναίσθητον, τοῦτο ὃ δὴ νόησις εἴληχεν ἐπισκοπεῖν· τὸ δὲ ὁμώνυμον ὅμοιόν τε ἐκείνῳ δεύτερον, αἰσθητόν, γεννητόν, πεφορημένον ἀεί, γιγνόμενόν τε ἔν τινι τόπῳ καὶ πάλιν ἐκεῖθεν ἀπολλύμενον, δόξῃ μετʼ αἰσθήσεως περιληπτόν· τρίτον δὲ αὖ γένος ὂν τὸ τῆς χώρας ἀεί, φθορὰν οὐ προσδεχόμενον, ἕδραν δὲ παρέχον ὅσα ἔχει γένεσιν πᾶσιν, αὐτὸ δὲ μετʼ ἀναισθησίας ἁπτὸν λογισμῷ τινι νόθῳ, μόγις πιστόν, πρὸς ὃ δὴ καὶ ὀνειροπολοῦμεν βλέποντες καί φαμεν ἀναγκαῖον εἶναί που τὸ ὂν ἅπαν ἔν τινι τόπῳ καὶ κατέχον χώραν τινά, τὸ δὲ μήτʼ ἐν γῇ μήτε που κατʼ οὐρανὸν οὐδὲν εἶναι.
52b. which admits not of destruction, and provides room for all things that have birth, itself being apprehensible by a kind of bastard reasoning by the aid of non-sensation, barely an object of belief; for when we regard this we dimly dream and affirm that it is somehow necessary that all that exists should exist in some spot and occupying some place, and that that which is neither on earth nor anywhere in the Heaven is nothing. So because of all these and other kindred notions, we are unable also on waking up to distinguish clearly the unsleeping and truly subsisting substance, owing to our dreamy condition, or to state the truth—how that it belongs to a copy—seeing that it has not for its own even that substance for which it came into being, but fleets ever as a phantom of something else—to come into existence in some other thing, clinging to existence as best it may, on pain of being nothing at all; whereas to the aid of the really existent there comes the accurately true argument, that so long as one thing is one thing, and another something different, neither of the two will ever come to exist in the other so that the same thing becomes simultaneously
52b. ταῦτα δὴ πάντα καὶ τούτων ἄλλα ἀδελφὰ καὶ περὶ τὴν ἄυπνον καὶ ἀληθῶς φύσιν ὑπάρχουσαν ὑπὸ ταύτης τῆς ὀνειρώξεως οὐ δυνατοὶ γιγνόμεθα ἐγερθέντες διοριζόμενοι τἀληθὲς λέγειν, ὡς εἰκόνι μέν, ἐπείπερ οὐδʼ αὐτὸ τοῦτο ἐφʼ ᾧ γέγονεν ἑαυτῆς ἐστιν, ἑτέρου δέ τινος ἀεὶ φέρεται φάντασμα, διὰ ταῦτα ἐν ἑτέρῳ προσήκει τινὶ γίγνεσθαι, οὐσίας ἁμωσγέπως ἀντεχομένην, ἢ μηδὲν τὸ παράπαν αὐτὴν εἶναι, τῷ δὲ ὄντως ὄντι βοηθὸς ὁ διʼ ἀκριβείας ἀληθὴς λόγος, ὡς ἕως ἄν τι τὸ μὲν ἄλλο ᾖ, τὸ δὲ ἄλλο, οὐδέτερον ἐν οὐδετέρῳ ποτὲ γενόμενον
52d. both one and two. Let this, then, be, according to my verdict, a reasoned account of the matter summarily stated,—that Being and Place and Becoming were existing, three distinct things, even before the Heaven came into existence; and that the Nurse of Becoming, being liquefied and ignified and receiving also the forms of earth and of air, and submitting to all the other affections which accompany these, exhibits every variety of appearance; but owing to being filled with potencies that are neither similar nor balanced, in no part of herself is she equally balanced, but sways unevenly in every part, and is herself shaken by these forms and shakes them in turn as she is moved.
52d. ἓν ἅμα ταὐτὸν καὶ δύο γενήσεσθον. οὗτος μὲν οὖν δὴ παρὰ τῆς ἐμῆς ψήφου λογισθεὶς ἐν κεφαλαίῳ δεδόσθω λόγος, ὄν τε καὶ χώραν καὶ γένεσιν εἶναι, τρία τριχῇ, καὶ πρὶν οὐρανὸν γενέσθαι· τὴν δὲ δὴ γενέσεως τιθήνην ὑγραινομένην καὶ πυρουμένην καὶ τὰς γῆς τε καὶ ἀέρος μορφὰς δεχομένην, καὶ ὅσα ἄλλα τούτοις πάθη συνέπεται πάσχουσαν, παντοδαπὴν μὲν ἰδεῖν φαίνεσθαι, διὰ δὲ τὸ μήθʼ ὁμοίων δυνάμεων μήτε ἰσορρόπων ἐμπίμπλασθαι κατʼ οὐδὲν αὐτῆς ἰσορροπεῖν, ἀλλʼ ἀνωμάλως πάντῃ ταλαντουμένην σείεσθαι μὲν ὑπʼ ἐκείνων αὐτήν, κινουμένην δʼ αὖ πάλιν ἐκεῖνα σείειν·
53. Tim. And the forms, as they are moved, fly continually in various directions and are dissipated; just as the particles that are shaken and winnowed by the sieves and other instruments used for the cleansing of corn fall in one place if they are solid and heavy, but fly off and settle elsewhere if they are spongy and light.
53. ΤΙ. τὰ δὲ κινούμενα ἄλλα ἄλλοσε ἀεὶ φέρεσθαι διακρινόμενα, ὥσπερ τὰ ὑπὸ τῶν πλοκάνων τε καὶ ὀργάνων τῶν περὶ τὴν τοῦ σίτου κάθαρσιν σειόμενα καὶ ἀνικμώμενα τὰ μὲν πυκνὰ καὶ βαρέα ἄλλῃ, τὰ δὲ μανὰ καὶ κοῦφα εἰς ἑτέραν ἵζει φερόμενα ἕδραν·
53a. So it was also with the Four Kinds when shaken by the Recipient: her motion, like an instrument which causes shaking, was separating farthest from one another the dissimilar, and pushing most closely together the similar; wherefore also these Kinds occupied different places even before that the Universe was organized and generated out of them. Before that time, in truth, all these things were in a state devoid of reason or measure, but when the work of setting in order this Universe was being undertaken, fire and water and earth and air, although possessing some traces of their own nature, were yet so disposed as everything is likely to be in the absence of God; and inasmuch as this was then their natural condition, God began by first marking them out into shapes by means of forms and numbers.
53a. τότε οὕτω τὰ τέτταρα γένη σειόμενα ὑπὸ τῆς δεξαμενῆς, κινουμένης αὐτῆς οἷον ὀργάνου σεισμὸν παρέχοντος, τὰ μὲν ἀνομοιότατα πλεῖστον αὐτὰ ἀφʼ αὑτῶν ὁρίζειν, τὰ δὲ ὁμοιότατα μάλιστα εἰς ταὐτὸν συνωθεῖν, διὸ δὴ καὶ χώραν ταῦτα ἄλλα ἄλλην ἴσχειν, πρὶν καὶ τὸ πᾶν ἐξ αὐτῶν διακοσμηθὲν γενέσθαι. καὶ τὸ μὲν δὴ πρὸ τούτου πάντα ταῦτʼ εἶχεν ἀλόγως καὶ ἀμέτρως·
53b. And that God constructed them, so far as He could, to be as fair and good as possible, whereas they had been otherwise,—this above all else must always be postulated in our account. Now, however, it is the disposition and origin of each of these Kinds which I must endeavor to explain to you in an exposition of an unusual type; yet, inasmuch as you have some acquaintance with the technical method which I must necessarily employ in my exposition, you will follow me.
53b. ὅτε δʼ ἐπεχειρεῖτο κοσμεῖσθαι τὸ πᾶν, πῦρ πρῶτον καὶ ὕδωρ καὶ γῆν καὶ ἀέρα, ἴχνη μὲν ἔχοντα αὑτῶν ἄττα, παντάπασί γε μὴν διακείμενα ὥσπερ εἰκὸς ἔχειν ἅπαν ὅταν ἀπῇ τινος θεός, οὕτω δὴ τότε πεφυκότα ταῦτα πρῶτον διεσχηματίσατο εἴδεσί τε καὶ ἀριθμοῖς. τὸ δὲ ᾗ δυνατὸν ὡς κάλλιστα ἄριστά τε ἐξ οὐχ οὕτως ἐχόντων τὸν θεὸν αὐτὰ συνιστάναι, παρὰ πάντα ἡμῖν ὡς ἀεὶ τοῦτο λεγόμενον ὑπαρχέτω· νῦν δʼ οὖν τὴν διάταξιν αὐτῶν ἐπιχειρητέον ἑκάστων καὶ γένεσιν ἀήθει λόγῳ πρὸς ὑμᾶς δηλοῦν, ἀλλὰ γὰρ ἐπεὶ μετέχετε τῶν κατὰ παίδευσιν ὁδῶν διʼ ὧν ἐνδείκνυσθαι τὰ λεγόμενα ἀνάγκη, συνέψεσθε.
53c. In the first place, then, it is plain I presume to everyone that fire and earth and water and air are solid bodies; and the form of a body, in every case, possesses depth also. Further, it is absolutely necessary that depth should be bounded by a plane surface; and the rectilinear plane is composed of triangles.
53c. πρῶτον μὲν δὴ πῦρ καὶ γῆ καὶ ὕδωρ καὶ ἀὴρ ὅτι σώματά ἐστι, δῆλόν που καὶ παντί· τὸ δὲ τοῦ σώματος εἶδος πᾶν καὶ βάθος ἔχει. τὸ δὲ βάθος αὖ πᾶσα ἀνάγκη τὴν ἐπίπεδον περιειληφέναι φύσιν· ἡ δὲ ὀρθὴ τῆς ἐπιπέδου βάσεως ἐκ τριγώνων συνέστηκεν. τὰ δὲ τρίγωνα πάντα ἐκ δυοῖν ἄρχεται τριγώνοιν, μίαν μὲν ὀρθὴν ἔχοντος ἑκατέρου γωνίαν, τὰς δὲ ὀξείας·
53d. Now all triangles derive their origin from two triangles, each having one angle right and the others acute; and the one of these triangles has on each side half a right angle marked off by equal sides, while the other has the right angle divided into unequal parts by unequal sides. These we lay down as the principles of fire and all the other bodies, proceeding according to a method in which the probable is combined with the necessary; but the principles which are still higher than these are known only to God and the man who is dear to God.
53d. ὧν τὸ μὲν ἕτερον ἑκατέρωθεν ἔχει μέρος γωνίας ὀρθῆς πλευραῖς ἴσαις διῃρημένης, τὸ δʼ ἕτερον ἀνίσοις ἄνισα μέρη νενεμημένης. ταύτην δὴ πυρὸς ἀρχὴν καὶ τῶν ἄλλων σωμάτων ὑποτιθέμεθα κατὰ τὸν μετʼ ἀνάγκης εἰκότα λόγον πορευόμενοι· τὰς δʼ ἔτι τούτων ἀρχὰς ἄνωθεν θεὸς οἶδεν καὶ ἀνδρῶν ὃς ἂν ἐκείνῳ φίλος ᾖ. δεῖ δὴ λέγειν ποῖα κάλλιστα σώματα γένοιτʼ ἂν τέτταρα, ἀνόμοια μὲν ἑαυτοῖς, δυνατὰ δὲ ἐξ ἀλλήλων αὐτῶν ἄττα διαλυόμενα γίγνεσθαι·
53e. We must now declare what will be the four fairest bodies, dissimilar to one another, but capable in part of being produced out of one another by means of dissolution; for if we succeed herein we shall grasp the truth concerning the generation of earth and fire and the mean proportionals. For to no one will we concede that fairer bodies than these, each distinct of its kind, are anywhere to be seen. Wherefore we must earnestly endeavor to frame together these four kinds of bodies which excel in beauty, and to maintain that we have apprehended their nature adequately.
53e. τούτου γὰρ τυχόντες ἔχομεν τὴν ἀλήθειαν γενέσεως πέρι γῆς τε καὶ πυρὸς τῶν τε ἀνὰ λόγον ἐν μέσῳ. τόδε γὰρ οὐδενὶ συγχωρησόμεθα, καλλίω τούτων ὁρώμενα σώματα εἶναί που καθʼ ἓν γένος ἕκαστον ὄν. τοῦτʼ οὖν προθυμητέον, τὰ διαφέροντα κάλλει σωμάτων τέτταρα γένη συναρμόσασθαι καὶ φάναι τὴν τούτων ἡμᾶς φύσιν ἱκανῶς εἰληφέναι.
54a. Tim. Now of the two triangles, the isosceles possesses one single nature, but the scalene an infinite number; and of these infinite natures we must select the fairest, if we mean to make a suitable beginning. If, then, anyone can claim that he has chosen one that is fairer for the construction of these bodies, he, as friend rather than foe, is the victor. We, however, shall pass over all the rest and postulate as the fairest of the triangles that triangle out of which, when two are conjoined, the equilateral triangle is constructed as a third.
54a. ΤΙ. τοῖν δὴ δυοῖν τριγώνοιν τὸ μὲν ἰσοσκελὲς μίαν εἴληχεν φύσιν, τὸ δὲ πρόμηκες ἀπεράντους· προαιρετέον οὖν αὖ τῶν ἀπείρων τὸ κάλλιστον, εἰ μέλλομεν ἄρξεσθαι κατὰ τρόπον. ἂν οὖν τις ἔχῃ κάλλιον ἐκλεξάμενος εἰπεῖν εἰς τὴν τούτων σύστασιν, ἐκεῖνος οὐκ ἐχθρὸς ὢν ἀλλὰ φίλος κρατεῖ· τιθέμεθα δʼ οὖν τῶν πολλῶν τριγώνων κάλλιστον ἕν, ὑπερβάντες τἆλλα, ἐξ οὗ τὸ ἰσόπλευρον τρίγωνον ἐκ τρίτου συνέστηκεν.
54b. The reason why is a longer story; but should anyone refute us and discover that it is not so, we begrudge him not the prize. Accordingly, let these two triangles be selected as those wherefrom are contrived the bodies of fire and of the other elements,— one being the isosceles, and the other that which always has the square on its greater side three times the square on the lesser side. Moreover, a point about which our previous statement was obscure must now be defined more clearly. It appeared as if the four Kinds, in being generated, all passed through one another into one another, but this appearance was deceptive.
54b. διότι δέ, λόγος πλείων· ἀλλὰ τῷ τοῦτο ἐλέγξαντι καὶ ἀνευρόντι δὴ οὕτως ἔχον κεῖται φίλια τὰ ἆθλα. προῃρήσθω δὴ δύο τρίγωνα ἐξ ὧν τό τε τοῦ πυρὸς καὶ τὰ τῶν ἄλλων σώματα μεμηχάνηται, τὸ μὲν ἰσοσκελές, τὸ δὲ τριπλῆν κατὰ δύναμιν ἔχον τῆς ἐλάττονος τὴν μείζω πλευρὰν ἀεί. τὸ δὴ πρόσθεν ἀσαφῶς ῥηθὲν νῦν μᾶλλον διοριστέον. τὰ γὰρ τέτταρα γένη διʼ ἀλλήλων εἰς ἄλληλα ἐφαίνετο πάντα γένεσιν ἔχειν, οὐκ ὀρθῶς φανταζόμενα· γίγνεται μὲν γὰρ ἐκ τῶν τριγώνων ὧν προῃρήμεθα γένη τέτταρα, τρία μὲν ἐξ ἑνὸς τοῦ τὰς πλευρὰς ἀνίσους ἔχοντος, τὸ δὲ τέταρτον ἓν μόνον ἐκ τοῦ ἰσοσκελοῦς τριγώνου συναρμοσθέν.
54c. For out of the triangles which we have selected four Kinds are generated, three of them out of that one triangle which has its sides unequal, and the fourth Kind alone composed of the isosceles triangle. Consequently, they are not all capable of being dissolved into one another so as to form a few large bodies composed of many small ones, or the converse; but three of them do admit of this process. For these three are all naturally compounded of one triangle, so that when the larger bodies are dissolved many small ones will form themselves from these same bodies, receiving the shapes that befit them;
54c. οὔκουν δυνατὰ πάντα εἰς ἄλληλα διαλυόμενα ἐκ πολλῶν σμικρῶν ὀλίγα μεγάλα καὶ τοὐναντίον γίγνεσθαι, τὰ δὲ τρία οἷόν τε· ἐκ γὰρ ἑνὸς ἅπαντα πεφυκότα λυθέντων τε τῶν μειζόνων πολλὰ σμικρὰ ἐκ τῶν αὐτῶν συστήσεται, δεχόμενα τὰ προσήκοντα ἑαυτοῖς σχήματα, καὶ σμικρὰ ὅταν αὖ πολλὰ κατὰ τὰ τρίγωνα διασπαρῇ, γενόμενος εἷς ἀριθμὸς ἑνὸς ὄγκου μέγα ἀποτελέσειεν ἂν ἄλλο εἶδος ἕν.
54d. and conversely, when many small bodies are resolved into their triangles they will produce, when unified, one single large mass of another Kind. So let thus much be declared concerning their generation into one another. In the next place we have to explain the form in which each Kind has come to exist and the numbers from which it is compounded. First will come that form which is primary and has the smallest components, and the element thereof is that triangle which has its hypotenuse twice as long as its lesser side. And when a pair of such triangles are joined along the line of the hypotenuse, and this is done thrice, by drawing the hypotenuses and the short sides together as to a center, there is produced from those triangles, six in number, one equilateral triangle.
54d. ταῦτα μὲν οὖν λελέχθω περὶ τῆς εἰς ἄλληλα γενέσεως· οἷον δὲ ἕκαστον αὐτῶν γέγονεν εἶδος καὶ ἐξ ὅσων συμπεσόντων ἀριθμῶν, λέγειν ἂν ἑπόμενον εἴη. ἄρξει δὴ τό τε πρῶτον εἶδος καὶ σμικρότατον συνιστάμενον, στοιχεῖον δʼ αὐτοῦ τὸ τὴν ὑποτείνουσαν τῆς ἐλάττονος πλευρᾶς διπλασίαν ἔχον μήκει· σύνδυο δὲ τοιούτων κατὰ διάμετρον συντιθεμένων καὶ τρὶς τούτου γενομένου, τὰς διαμέτρους καὶ τὰς βραχείας πλευρὰς εἰς ταὐτὸν ὡς κέντρον ἐρεισάντων, ἓν ἰσόπλευρον τρίγωνον ἐξ ἓξ τὸν ἀριθμὸν ὄντων γέγονεν.
55. Tim. And when four equilateral triangles are combined so that three plane angles meet in a point, they form one solid angle, which comes next in order to the most obtuse of the plane angles.
55. ΤΙ. τρίγωνα δὲ ἰσόπλευρα συνιστάμενα τέτταρα κατὰ σύντρεις ἐπιπέδους γωνίας μίαν στερεὰν γωνίαν ποιεῖ, τῆς ἀμβλυτάτης τῶν ἐπιπέδων γωνιῶν ἐφεξῆς γεγονυῖαν·
55a. And when four such angles are produced, the first solid figure is constructed, which divides the whole of the circumscribed sphere into equal and similar parts. And the second solid is formed from the same triangles, but constructed out of eight equilateral triangles, which produce one solid angle out of four planes; and when six such solid angles have been formed, the second body in turn is completed.
55a. τοιούτων δὲ ἀποτελεσθεισῶν τεττάρων πρῶτον εἶδος στερεόν, ὅλου περιφεροῦς διανεμητικὸν εἰς ἴσα μέρη καὶ ὅμοια, συνίσταται. δεύτερον δὲ ἐκ μὲν τῶν αὐτῶν τριγώνων, κατὰ δὲ ἰσόπλευρα τρίγωνα ὀκτὼ συστάντων, μίαν ἀπεργασαμένων στερεὰν γωνίαν ἐκ τεττάρων ἐπιπέδων· καὶ γενομένων ἓξ τοιούτων τὸ δεύτερον αὖ σῶμα οὕτως ἔσχεν τέλος. τὸ δὲ τρίτον ἐκ δὶς ἑξήκοντα τῶν στοιχείων συμπαγέντων, στερεῶν δὲ γωνιῶν δώδεκα, ὑπὸ πέντε ἐπιπέδων τριγώνων ἰσοπλεύρων περιεχομένης ἑκάστης, εἴκοσι βάσεις ἔχον ἰσοπλεύρους τριγώνους γέγονεν.
55b. And the third solid is composed of twice sixty of the elemental triangles conjoined, and of twelve solid angles, each contained by five plane equilateral triangles, and it has, by its production, twenty equilateral triangular bases. Now the first of the elemental triangles ceased acting when it had generated these three solids, the substance of the fourth Kind being generated by the isosceles triangle. Four of these combined, with their right angles drawn together to the center, produced one equilateral quadrangle; and six such quadrangles, when joined together, formed eight solid angles, each composed of three plane right angles; and the shape of the body thus constructed was cubic, having six plane equilateral quadrangular bases.
55b. καὶ τὸ μὲν ἕτερον ἀπήλλακτο τῶν στοιχείων ταῦτα γεννῆσαν, τὸ δὲ ἰσοσκελὲς τρίγωνον ἐγέννα τὴν τοῦ τετάρτου φύσιν, κατὰ τέτταρα συνιστάμενον, εἰς τὸ κέντρον τὰς ὀρθὰς γωνίας συνάγον, ἓν ἰσόπλευρον τετράγωνον ἀπεργασάμενον· ἓξ δὲ τοιαῦτα συμπαγέντα γωνίας ὀκτὼ στερεὰς ἀπετέλεσεν, κατὰ τρεῖς ἐπιπέδους ὀρθὰς συναρμοσθείσης ἑκάστης·
55c. And seeing that there still remained one other compound figure, the fifth, God used it up for the Universe in his decoration thereof. Now in reasoning about all these things, a man might question whether he ought to affirm the existence of an infinite diversity of Universes or a limited number; and if he questioned aright he would conclude that the doctrine of an infinite diversity is that of a man unversed in matters wherein he ought to be versed; but the question whether they ought really to be described as one Universe or five is one which might with more reason give us pause.
55c. τὸ δὲ σχῆμα τοῦ συστάντος σώματος γέγονεν κυβικόν, ἓξ ἐπιπέδους τετραγώνους ἰσοπλεύρους βάσεις ἔχον. ἔτι δὲ οὔσης συστάσεως μιᾶς πέμπτης, ἐπὶ τὸ πᾶν ὁ θεὸς αὐτῇ κατεχρήσατο ἐκεῖνο διαζωγραφῶν. ἃ δή τις εἰ πάντα λογιζόμενος ἐμμελῶς ἀποροῖ πότερον ἀπείρους χρὴ κόσμους εἶναι λέγειν ἢ πέρας ἔχοντας, τὸ μὲν ἀπείρους ἡγήσαιτʼ ἂν ὄντως ἀπείρου τινὸς εἶναι δόγμα ὧν ἔμπειρον χρεὼν εἶναι, πότερον δὲ ἕνα ἢ πέντε αὐτοὺς ἀληθείᾳ πεφυκότας λέγειν ποτὲ προσήκει, μᾶλλον ἂν ταύτῃ στὰς εἰκότως διαπορήσαι.
55d. Now our view declares the Universe to be essentially one, in accordance with the probable account; but another man, considering other facts, will hold a different opinion. Him, however, we must let pass. But as for the Kinds which have now been generated by our argument, let us assign them severally to fire and earth and water and air. To earth let us give the cubic form; for of the four Kinds earth is the most immobile and the most plastic body, and of necessity the body which has the most stable bases must be pre-eminently of this character.
55d. τὸ μὲν οὖν δὴ παρʼ ἡμῶν ἕνα αὐτὸν κατὰ τὸν εἰκότα λόγον πεφυκότα μηνύει θεόν, ἄλλος δὲ εἰς ἄλλα πῃ βλέψας ἕτερα δοξάσει. καὶ τοῦτον μὲν μεθετέον, τὰ δὲ γεγονότα νῦν τῷ λόγῳ γένη διανείμωμεν εἰς πῦρ καὶ γῆν καὶ ὕδωρ καὶ ἀέρα. γῇ μὲν δὴ τὸ κυβικὸν εἶδος δῶμεν·
55e. Now of the triangles we originally assumed, the basis formed by equal sides is of its nature more stable than that formed by unequal sides; and of the plane surfaces which are compounded of these several triangles, the equilateral quadrangle, both in its parts and as a whole, has a more stable base than the equilateral triangle.
55e. ἀκινητοτάτη γὰρ τῶν τεττάρων γενῶν γῆ καὶ τῶν σωμάτων πλαστικωτάτη, μάλιστα δὲ ἀνάγκη γεγονέναι τοιοῦτον τὸ τὰς βάσεις ἀσφαλεστάτας ἔχον· βάσις δὲ ἥ τε τῶν κατʼ ἀρχὰς τριγώνων ὑποτεθέντων ἀσφαλεστέρα κατὰ φύσιν ἡ τῶν ἴσων πλευρῶν τῆς τῶν ἀνίσων, τό τε ἐξ ἑκατέρου συντεθὲν ἐπίπεδον ἰσόπλευρον ἰσοπλεύρου τετράγωνον τριγώνου κατά τε μέρη καὶ καθʼ ὅλον στασιμωτέρως ἐξ ἀνάγκης βέβηκεν. ΤΙ. διὸ γῇ μὲν τοῦτο ἀπονέμοντες τὸν εἰκότα λόγον διασῴζομεν, ὕδατι δʼ αὖ τῶν λοιπῶν τὸ δυσκινητότατον εἶδος, τὸ δʼ εὐκινητότατον πυρί, τὸ δὲ μέσον ἀέρι·
56a. Tim. Wherefore, we are preserving the probable account when we assign this figure to earth, and of the remaining figures the least mobile to water, and the most mobile to fire, and the intermediate figure to air; and, further, when we assign the smallest body to fire, and the greatest to water, and the intermediate to air; and again, the first in point of sharpness to fire, the second to air, and the third to water. As regards all these forms, that which has the fewest bases must necessarily be the most mobile, since it is in all ways the sharpest and most acute of all; and it must also be the lightest, since it is composed of the fewest identical parts; and the second comes second in point of these same qualities, and the third third.
56a. καὶ τὸ μὲν σμικρότατον σῶμα πυρί, τὸ δʼ αὖ μέγιστον ὕδατι, τὸ δὲ μέσον ἀέρι· καὶ τὸ μὲν ὀξύτατον αὖ πυρί, τὸ δὲ δεύτερον ἀέρι, τὸ δὲ τρίτον ὕδατι. ταῦτʼ οὖν δὴ πάντα, τὸ μὲν ἔχον ὀλιγίστας βάσεις εὐκινητότατον ἀνάγκη πεφυκέναι, τμητικώτατόν τε καὶ ὀξύτατον ὂν πάντῃ πάντων, ἔτι τε ἐλαφρότατον, ἐξ ὀλιγίστων συνεστὸς τῶν αὐτῶν μερῶν·
56b. Thus, in accordance with the right account and the probable, that solid which has taken the form of a pyramid shall be the element and seed of fire; the second in order of generation we shall affirm to be air, and the third water. Now one must conceive all these to be so small that none of them, when taken singly each in its several kind, is seen by us, but when many are collected together their masses are seen.
56b. τὸ δὲ δεύτερον δευτέρως τὰ αὐτὰ ταῦτʼ ἔχειν, τρίτως δὲ τὸ τρίτον. ἔστω δὴ κατὰ τὸν ὀρθὸν λόγον καὶ κατὰ τὸν εἰκότα τὸ μὲν τῆς πυραμίδος στερεὸν γεγονὸς εἶδος πυρὸς στοιχεῖον καὶ σπέρμα· τὸ δὲ δεύτερον κατὰ γένεσιν εἴπωμεν ἀέρος, τὸ δὲ τρίτον ὕδατος. πάντα οὖν δὴ ταῦτα δεῖ διανοεῖσθαι σμικρὰ οὕτως, ὡς καθʼ ἓν ἕκαστον μὲν τοῦ γένους ἑκάστου διὰ σμικρότητα οὐδὲν ὁρώμενον ὑφʼ ἡμῶν, συναθροισθέντων δὲ πολλῶν τοὺς ὄγκους αὐτῶν ὁρᾶσθαι·
56c. And, moreover, as regards the numerical proportions which govern their masses and motions and their other qualities, we must conceive that God realized these everywhere with exactness, in so far as the nature of Necessity submitted voluntarily or under persuasion, and thus ordered all in harmonious proportion. From all that we have hitherto said about these Kinds, they will, in all likelihood, behave themselves as follows.
56c. καὶ δὴ καὶ τὸ τῶν ἀναλογιῶν περί τε τὰ πλήθη καὶ τὰς κινήσεις καὶ τὰς ἄλλας δυνάμεις πανταχῇ τὸν θεόν, ὅπῃπερ ἡ τῆς ἀνάγκης ἑκοῦσα πεισθεῖσά τε φύσις ὑπεῖκεν, ταύτῃ πάντῃ διʼ ἀκριβείας ἀποτελεσθεισῶν ὑπʼ αὐτοῦ συνηρμόσθαι ταῦτα ἀνὰ λόγον. ἐκ δὴ πάντων ὧνπερ τὰ γένη προειρήκαμεν ὧδʼ ἂν κατὰ τὸ εἰκὸς μάλιστʼ ἂν ἔχοι.
56d. Earth will keep moving when it happens to meet with fire and has been dissolved by its acuteness, whether this dissolution takes place in pure fire or in a mass of air or of water; and this motion will continue until the particles of earth happen to meet together somewhere and reunite one with another, when they become earth again; for assuredly earth will never change into another form. But water, when broken up by fire or even by air, is capable of becoming a compound of one corpuscle of fire with two of air;
56d. γῆ μὲν συντυγχάνουσα πυρὶ διαλυθεῖσά τε ὑπὸ τῆς ὀξύτητος αὐτοῦ φέροιτʼ ἄν, εἴτʼ ἐν αὐτῷ πυρὶ λυθεῖσα εἴτʼ ἐν ἀέρος εἴτʼ ἐν ὕδατος ὄγκῳ τύχοι, μέχριπερ ἂν αὐτῆς πῃ συντυχόντα τὰ μέρη, πάλιν συναρμοσθέντα αὐτὰ αὑτοῖς, γῆ γένοιτο—οὐ γὰρ εἰς ἄλλο γε εἶδος ἔλθοι ποτʼ ἄν—ὕδωρ δὲ ὑπὸ πυρὸς μερισθέν, εἴτε καὶ ὑπʼ ἀέρος, ἐγχωρεῖ γίγνεσθαι συστάντα ἓν μὲν πυρὸς σῶμα, δύο δὲ ἀέρος·
56e. and the fractions of air which come from the dissolving of one particle will form two corpuscles of fire. And again, when a small quantity of fire is enclosed by a large quantity of air and water, or of earth, and moves within them as they rush along, and is defeated in its struggle and broken up, then two corpuscles of fire unite to make one form of air. And when air is defeated and disintegrated, from two whole forms of air and a half, one whole form of water will be compounded.
56e. τὰ δὲ ἀέρος τμήματα ἐξ ἑνὸς μέρους διαλυθέντος δύʼ ἂν γενοίσθην σώματα πυρός. καὶ πάλιν, ὅταν ἀέρι πῦρ ὕδασίν τε ἤ τινι γῇ περιλαμβανόμενον ἐν πολλοῖς ὀλίγον, κινούμενον ἐν φερομένοις, μαχόμενον καὶ νικηθὲν καταθραυσθῇ, δύο πυρὸς σώματα εἰς ἓν συνίστασθον εἶδος ἀέρος· καὶ κρατηθέντος ἀέρος κερματισθέντος τε ἐκ δυοῖν ὅλοιν καὶ ἡμίσεος ὕδατος εἶδος ἓν ὅλον ἔσται συμπαγές. ΤΙ. ὧδε γὰρ δὴ λογισώμεθα αὐτὰ πάλιν, ὡς ὅταν ἐν πυρὶ λαμβανόμενον τῶν ἄλλων ὑπʼ αὐτοῦ τι γένος τῇ τῶν γωνιῶν καὶ κατὰ τὰς πλευρὰς ὀξύτητι τέμνηται, συστὰν μὲν εἰς τὴν ἐκείνου φύσιν πέπαυται τεμνόμενον—τὸ γὰρ ὅμοιον καὶ ταὐτὸν αὑτῷ γένος ἕκαστον οὔτε τινὰ μεταβολὴν ἐμποιῆσαι δυνατὸν οὔτε τι παθεῖν ὑπὸ τοῦ κατὰ ταὐτὰ ὁμοίως τε ἔχοντος—ἕως δʼ ἂν εἰς ἄλλο τι γιγνόμενον ἧττον ὂν κρείττονι μάχηται, λυόμενον οὐ παύεται.
57a. Tim. Once again let us reason out their character in this way. Whenever any of the other Kinds is caught within fire it is cut up thereby, owing to the acuteness of its angles and of the line of its sides, but when it has been re-composed into the substance of fire it ceases to be cut; for the Kind that is similar and uniform is in no case able either to cause any change in, or to suffer any affection from, a Kind which is in a uniform and similar state; but so long as, in the course of its passage into another form, it is a weaker body fighting against a stronger, it is continually being dissolved. And again, whenever a few of the smaller corpuscles, being caught within a great number of larger corpuscles, are broken up and quenched, then, if they consent to be re-compounded into the shape of the victorious Kind, they cease to be quenched, and air is produced out of fire, and out of air water; but if they fight against combining with these or with any of the other Kinds, they do not cease from dissolution until either they are driven out to their own kindred, by means of this impact and dissolution, or else they are defeated and, instead of many forms, assume one form similar to the victorious Kind, and continue dwelling therewith as a united family. Moreover, it is owing to these affections that they all interchange their places; for while the bulk of each Kind keeps apart in a region of its own because of the motion of the Recipient, yet those corpuscles which from time to time become dissimilar to themselves and similar to others are carried, because of the shaking, towards the region which belongs to those corpuscles whereto they have been assimilated. Such are the causes which account for the generation of all the unmixed and primary bodies. But within these four Kinds other classes exist, whereof the cause must be sought in the construction of each of the two elemental triangles, each such construction having originally produced not merely a triangle of one definite size, but larger and smaller triangles of sizes as numerous as are the classes within the Kinds.
57a. τά τε αὖ σμικρότερα ὅταν ἐν τοῖς μείζοσιν πολλοῖς περιλαμβανόμενα ὀλίγα διαθραυόμενα κατασβεννύηται, συνίστασθαι μὲν ἐθέλοντα εἰς τὴν τοῦ κρατοῦντος ἰδέαν πέπαυται κατασβεννύμενα γίγνεταί τε ἐκ πυρὸς ἀήρ, ἐξ ἀέρος ὕδωρ· ἐὰν δʼ εἰς ταὐτὰ ἴῃ καὶ τῶν ἄλλων τι συνιὸν γενῶν μάχηται, λυόμενα οὐ παύεται, πρὶν ἢ παντάπασιν ὠθούμενα καὶ διαλυθέντα ἐκφύγῃ πρὸς τὸ συγγενές, ἢ νικηθέντα, ἓν ἐκ πολλῶν ὅμοιον τῷ κρατήσαντι γενόμενον, αὐτοῦ σύνοικον μείνῃ. καὶ δὴ καὶ κατὰ ταῦτα τὰ παθήματα διαμείβεται τὰς χώρας ἅπαντα· διέστηκεν μὲν γὰρ τοῦ γένους ἑκάστου τὰ πλήθη κατὰ τόπον ἴδιον διὰ τὴν τῆς δεχομένης κίνησιν, τὰ δὲ ἀνομοιούμενα ἑκάστοτε ἑαυτοῖς, ἄλλοις δὲ ὁμοιούμενα, φέρεται διὰ τὸν σεισμὸν πρὸς τὸν ἐκείνων οἷς ἂν ὁμοιωθῇ τόπον. ὅσα μὲν οὖν ἄκρατα καὶ πρῶτα σώματα διὰ τοιούτων αἰτιῶν γέγονεν· τὸ δʼ ἐν τοῖς εἴδεσιν αὐτῶν ἕτερα ἐμπεφυκέναι γένη τὴν ἑκατέρου τῶν στοιχείων αἰτιατέον σύστασιν, μὴ μόνον ἓν ἑκατέραν μέγεθος ἔχον τὸ τρίγωνον φυτεῦσαι κατʼ ἀρχάς, ἀλλʼ ἐλάττω τε καὶ μείζω, τὸν ἀριθμὸν δὲ ἔχοντα τοσοῦτον ὅσαπερ ἂν ᾖ τἀν τοῖς εἴδεσι γένη.
57d. Consequently, when these are combined amongst themselves and with one another they are infinite in their variety; and this variety must be kept in view by those who purpose to employ probable reasoning concerning Nature. Now, unless we can arrive at some agreed conclusion concerning Motion and Rest, as to how and under what conditions they come about, our subsequent argument will be greatly hampered.
57d. διὸ δὴ συμμειγνύμενα αὐτά τε πρὸς αὑτὰ καὶ πρὸς ἄλληλα τὴν ποικιλίαν ἐστὶν ἄπειρα· ἧς δὴ δεῖ θεωροὺς γίγνεσθαι τοὺς μέλλοντας περὶ φύσεως εἰκότι λόγῳ χρήσεσθαι. κινήσεως οὖν στάσεώς τε πέρι, τίνα τρόπον καὶ μεθʼ ὧντινων γίγνεσθον, εἰ μή τις διομολογήσεται, πόλλʼ ἂν εἴη ἐμποδὼν τῷ κατόπισθεν λογισμῷ.
57e. The facts about them have already been stated in part; but in addition thereto we must state further that motion never consents to exist within uniformity. For it is difficult, or rather impossible, for that which is to be moved to exist without that which is to move, or that which is to move without that which is to be moved; but in the absence of these there is no motion, and that these should ever be uniform is a thing impossible.
57e. τὰ μὲν οὖν ἤδη περὶ αὐτῶν εἴρηται, πρὸς δʼ ἐκείνοις ἔτι τάδε, ἐν μὲν ὁμαλότητι μηδέποτε ἐθέλειν κίνησιν ἐνεῖναι. τὸ γὰρ κινησόμενον ἄνευ τοῦ κινήσοντος ἢ τὸ κινῆσον ἄνευ τοῦ κινησομένου χαλεπόν, μᾶλλον δὲ ἀδύνατον, εἶναι· κίνησις δὲ οὐκ ἔστιν τούτων ἀπόντων, ταῦτα δὲ ὁμαλὰ εἶναί ποτε ἀδύνατον.
58. Tim. Accordingly, we must always place rest in uniformity, and motion in non-uniformity; and the cause of the non-uniform nature lies in inequality.
58. ΤΙ. οὕτω δὴ στάσιν μὲν ἐν ὁμαλότητι, κίνησιν δὲ εἰς ἀνωμαλότητα ἀεὶ τιθῶμεν·
58a. Now we have explained the origin of inequality; but we have not declared how it is that these bodies are not separated according to their several Kinds, and cease not from their motion and passage one through another. Wherefore, we shall once more expound the matter as follows. The revolution of the All, since it comprehends the Kinds, compresses them all, seeing that it is circular and tends naturally to come together to itself; and thus it suffers no void place to be left.
58a. αἰτία δὲ ἀνισότης αὖ τῆς ἀνωμάλου φύσεως. ἀνισότητος δὲ γένεσιν μὲν διεληλύθαμεν· πῶς δέ ποτε οὐ κατὰ γένη διαχωρισθέντα ἕκαστα πέπαυται τῆς διʼ ἀλλήλων κινήσεως καὶ φορᾶς, οὐκ εἴπομεν. ὧδε οὖν πάλιν ἐροῦμεν. ἡ τοῦ παντὸς περίοδος, ἐπειδὴ συμπεριέλαβεν τὰ γένη, κυκλοτερὴς οὖσα καὶ πρὸς αὑτὴν πεφυκυῖα βούλεσθαι συνιέναι, σφίγγει πάντα καὶ κενὴν χώραν οὐδεμίαν ἐᾷ λείπεσθαι. διὸ δὴ πῦρ μὲν εἰς ἅπαντα διελήλυθε μάλιστα, ἀὴρ δὲ δεύτερον, ὡς λεπτότητι δεύτερον ἔφυ, καὶ τἆλλα ταύτῃ·
58b. Wherefore, fire most of all has permeated all things, and in a second degree air, as it is by nature second in fineness; and so with the rest; for those that have the largest constituent parts have the largest void left in their construction, and those that have the smallest the least. Thus the tightening of the compression forces together the small bodies into the void intervals of the large. Therefore, when small bodies are placed beside large, and the smaller disintegrate the larger while the larger unite the smaller, they all shift up and down towards their own proper regions; for the change in their several sizes causes their position in space also to change.
58b. τὰ γὰρ ἐκ μεγίστων μερῶν γεγονότα μεγίστην κενότητα ἐν τῇ συστάσει παραλέλοιπεν, τὰ δὲ σμικρότατα ἐλαχίστην. ἡ δὴ τῆς πιλήσεως σύνοδος τὰ σμικρὰ εἰς τὰ τῶν μεγάλων διάκενα συνωθεῖ. σμικρῶν οὖν παρὰ μεγάλα τιθεμένων καὶ τῶν ἐλαττόνων τὰ μείζονα διακρινόντων, τῶν δὲ μειζόνων ἐκεῖνα συγκρινόντων, πάντʼ ἄνω κάτω μεταφέρεται πρὸς τοὺς ἑαυτῶν τόπους·
58c. And since in this way and for these reasons the production of non-uniformity is perpetually maintained, it brings about unceasingly, both now and for the future, the perpetual motion of these bodies. In the next place, we must observe that there are many kinds of fire: for example, there is flame; and the kind issuing from flame, which does not burn but supplies light to the eyes; and the kind which, when the flame is quenched, is left behind among the embers.
58c. μεταβάλλον γὰρ τὸ μέγεθος ἕκαστον καὶ τὴν τόπων μεταβάλλει στάσιν. οὕτω δὴ διὰ ταῦτά τε ἡ τῆς ἀνωμαλότητος διασῳζομένη γένεσις ἀεὶ τὴν ἀεὶ κίνησιν τούτων οὖσαν ἐσομένην τε ἐνδελεχῶς παρέχεται. μετὰ δὴ ταῦτα δεῖ νοεῖν ὅτι πυρός τε γένη πολλὰ γέγονεν, οἷον φλὸξ τό τε ἀπὸ τῆς φλογὸς ἀπιόν, ὃ κάει μὲν οὔ, φῶς δὲ τοῖς ὄμμασιν παρέχει, τό τε φλογὸς ἀποσβεσθείσης ἐν τοῖς διαπύροις καταλειπόμενον αὐτοῦ·
58d. So likewise of air, there is the most translucent kind which is called by the name of aether, and the most opaque which is mist and darkness, and other species without a name, which are produced by reason of the inequality of the triangles. The kinds of water are, primarily, two, the one being the liquid, the other the fusible kind. Now the liquid kind, inasmuch as it partakes of those small particles of water which are unequal, is mobile both in itself and by external force owing to its non-uniformity and the shape of its figure. But the other kind, which is composed of large and uniform particles, is more stable than the first and is heavy, being solidified by its uniformity; but when fire enters and dissolves it, this causes it to abandon its uniformity, and this being lost it partakes more largely in motion; and when it has become mobile it is pushed by the adjacent air and extended upon the earth; and for each of these modifications it has received a descriptive name—“melting” for the disintegration of its masses, and for its extension over the earth “fluidity.” Tim. Again, since the fire on issuing from the water does not pass into a void but presses on the adjacent air, this in turn compresses the liquid mass which is still mobile into the abodes of the fire and combines it with itself; and the mass, being this, is compressed and recovering again its uniformity, because of the departure of the fire, the author of its non-uniformity, returns to its state of self-identity.
58d. κατὰ ταὐτὰ δὲ ἀέρος, τὸ μὲν εὐαγέστατον ἐπίκλην αἰθὴρ καλούμενος, ὁ δὲ θολερώτατος ὁμίχλη τε καὶ σκότος, ἕτερά τε ἀνώνυμα εἴδη, γεγονότα διὰ τὴν τῶν τριγώνων ἀνισότητα. τὰ δὲ ὕδατος διχῇ μὲν πρῶτον, τὸ μὲν ὑγρόν, τὸ δὲ χυτὸν γένος αὐτοῦ. τὸ μὲν οὖν ὑγρὸν διὰ τὸ μετέχον εἶναι τῶν γενῶν τῶν ὕδατος ὅσα σμικρά, ἀνίσων ὄντων, κινητικὸν αὐτό τε καθʼ αὑτὸ καὶ ὑπʼ ἄλλου διὰ τὴν ἀνωμαλότητα καὶ τὴν τοῦ σχήματος ἰδέαν γέγονεν· τὸ δὲ ἐκ μεγάλων καὶ ὁμαλῶν στασιμώτερον μὲν ἐκείνου καὶ βαρὺ πεπηγὸς ὑπὸ ὁμαλότητός ἐστιν, ὑπὸ δὲ πυρὸς εἰσιόντος καὶ διαλύοντος αὐτὸ τὴν ὁμαλότητα ἀποβάλλει, ταύτην δὲ ἀπολέσαν μετίσχει μᾶλλον κινήσεως, γενόμενον δὲ εὐκίνητον, ὑπὸ τοῦ πλησίον ἀέρος ὠθούμενον καὶ κατατεινόμενον ἐπὶ γῆν, τήκεσθαι μὲν τὴν τῶν ὄγκων καθαίρεσιν, ῥοὴν δὲ τὴν κατάτασιν ἐπὶ γῆν ἐπωνυμίαν ἑκατέρου τοῦ πάθους ἔλαβεν.
59a. And this cessation of the fire is termed “cooling,” and the combination which follows on its departure “solidification.” Of all the kinds of water which we have termed “fusible,” the densest is produced from the finest and most uniform particles: this is a kind of unique form, tinged with a glittering and yellow hue, even that most precious of possessions, “gold,” which has been strained through stones and solidified. And the off-shoot of gold, which is very hard because of its density and black in color, is called “adamant.” And the kind which closely resembles gold in its particles but has more forms than one, and in density is more dense than gold, and partakes of small and fine portions of earth so that it is harder, while it is also lighter owing to its having large interstices within it,—this particular kind of the bright and solid waters, being compounded thus, is termed “bronze.”
59a. ΤΙ. πάλιν δʼ ἐκπίπτοντος αὐτόθεν τοῦ πυρός, ἅτε οὐκ εἰς κενὸν ἐξιόντος, ὠθούμενος ὁ πλησίον ἀὴρ εὐκίνητον ὄντα ἔτι τὸν ὑγρὸν ὄγκον εἰς τὰς τοῦ πυρὸς ἕδρας συνωθῶν αὐτὸν αὑτῷ συμμείγνυσιν· ὁ δὲ συνωθούμενος ἀπολαμβάνων τε τὴν ὁμαλότητα πάλιν, ἅτε τοῦ τῆς ἀνωμαλότητος δημιουργοῦ πυρὸς ἀπιόντος, εἰς ταὐτὸν αὑτῷ καθίσταται. καὶ τὴν μὲν τοῦ πυρὸς ἀπαλλαγὴν ψῦξιν, τὴν δὲ σύνοδον ἀπελθόντος ἐκείνου πεπηγὸς εἶναι γένος προσερρήθη. τούτων δὴ πάντων ὅσα χυτὰ προσείπομεν ὕδατα, τὸ μὲν ἐκ λεπτοτάτων καὶ ὁμαλωτάτων πυκνότατον γιγνόμενον, μονοειδὲς γένος, στίλβοντι καὶ ξανθῷ χρώματι κοινωθέν, τιμαλφέστατον κτῆμα χρυσὸς ἠθημένος διὰ πέτρας ἐπάγη· χρυσοῦ δὲ ὄζος, διὰ πυκνότητα σκληρότατον ὂν καὶ μελανθέν, ἀδάμας ἐκλήθη. τὸ δʼ ἐγγὺς μὲν χρυσοῦ τῶν μερῶν, εἴδη δὲ πλείονα ἑνὸς ἔχον, πυκνότητι δέ, τῇ μὲν χρυσοῦ πυκνότερον ὄν, καὶ γῆς μόριον ὀλίγον καὶ λεπτὸν μετασχόν, ὥστε σκληρότερον εἶναι, τῷ δὲ μεγάλα ἐντὸς αὑτοῦ διαλείμματα ἔχειν κουφότερον, τῶν λαμπρῶν πηκτῶν τε ἓν γένος ὑδάτων χαλκὸς συσταθεὶς γέγονεν·
59c. And the portion of earth that is mixed therewith becomes distinct by itself, when both grow old and separate again-each from the other; and then it is named “rust.” And the rest of such phenomena it is no longer difficult to explain in full, if one aims at framing a description that is probable. For as regards this, whenever for the sake of recreation a man lays aside arguments concerning eternal Realities and considers probable accounts of Becoming, gaining thereby a pleasure not to be repented of, he provides for his life a pastime that is both moderate and sensible.
59c. τὸ δʼ ἐκ γῆς αὐτῷ μειχθέν, ὅταν παλαιουμένω διαχωρίζησθον πάλιν ἀπʼ ἀλλήλων, ἐκφανὲς καθʼ αὑτὸ γιγνόμενον ἰὸς λέγεται. τἆλλα δὲ τῶν τοιούτων οὐδὲν ποικίλον ἔτι διαλογίσασθαι τὴν τῶν εἰκότων μύθων μεταδιώκοντα ἰδέαν· ἣν ὅταν τις ἀναπαύσεως ἕνεκα τοὺς περὶ τῶν ὄντων ἀεὶ καταθέμενος λόγους, τοὺς γενέσεως πέρι διαθεώμενος εἰκότας ἀμεταμέλητον ἡδονὴν κτᾶται, μέτριον ἂν ἐν τῷ βίῳ παιδιὰν καὶ φρόνιμον ποιοῖτο.
59d. To this pastime let us now give free play, and proceed to expound in order the subsequent probabilities concerning these same phenomena in the following way. The water that is mixed with fire, which is fine and fluid, is termed “fluid,” owing to its motion and the way it rolls over the earth. Also it is soft owing to the fact that its bases, being less stable than those of earth, give way. When this kind is separated off from fire and air and isolated it becomes more uniform, but because of their outflow it is compressed upon itself; and when it is thus solidified, the part of it above the earth which is most affected by this process is termed “hail,” and the part upon the earth “ice” and the part which is less affected and is still only half-solid is called snow when it is above the earth, but when it is upon the earth and solidified out of dew it is called “hoar-frost.”
59d. ταύτῃ δὴ καὶ τὰ νῦν ἐφέντες τὸ μετὰ τοῦτο τῶν αὐτῶν πέρι τὰ ἑξῆς εἰκότα δίιμεν τῇδε. τὸ πυρὶ μεμειγμένον ὕδωρ, ὅσον λεπτὸν ὑγρόν τε διὰ τὴν κίνησιν καὶ τὴν ὁδὸν ἣν κυλινδούμενον ἐπὶ γῆς ὑγρὸν λέγεται, μαλακόν τε αὖ τῷ τὰς βάσεις ἧττον ἑδραίους οὔσας ἢ τὰς γῆς ὑπείκειν, τοῦτο ὅταν πυρὸς ἀποχωρισθὲν ἀέρος τε μονωθῇ, γέγονεν μὲν ὁμαλώτερον, συνέωσται δὲ ὑπὸ τῶν ἐξιόντων εἰς αὑτό, παγέν τε οὕτως τὸ μὲν ὑπὲρ γῆς μάλιστα παθὸν ταῦτα χάλαζα, τὸ δʼ ἐπὶ γῆς κρύσταλλος, τὸ δὲ ἧττον, ἡμιπαγές τε ὂν ἔτι, τὸ μὲν ὑπὲρ γῆς αὖ χιών, τὸ δʼ ἐπὶ γῆς συμπαγὲν ἐκ δρόσου γενόμενον πάχνη λέγεται.
60. Tim. Now as regards most forms of water that are intermingled one with another, the kind as a whole, consisting of water that has been strained through earth-grown plants, is called “sap”; but inasmuch as the several sorts have become dissimilar owing to intermixture, most of the kinds thus produced are unnamed. Four of these kinds, however, being fiery and specially conspicuous, have received names. Of these, that which is heating to the soul as well as the body is called “wine”; that which is smooth and divisive of the vision, and therefore bright to look upon and gleaming and glistening in appearance, is the species “oil,” including pitch and castor oil and olive oil itself and all the others that are of the same character;
60. ΤΙ. τὰ δὲ δὴ πλεῖστα ὑδάτων εἴδη μεμειγμένα ἀλλήλοις—σύμπαν μὲν τὸ γένος, διὰ τῶν ἐκ γῆς φυτῶν ἠθημένα, χυμοὶ λεγόμενοι—διὰ δὲ τὰς μείξεις ἀνομοιότητα ἕκαστοι σχόντες τὰ μὲν ἄλλα πολλὰ ἀνώνυμα γένη παρέσχοντο, τέτταρα δὲ ὅσα ἔμπυρα εἴδη, διαφανῆ μάλιστα γενόμενα, εἴληφεν ὀνόματα αὐτῶν, τὸ μὲν τῆς ψυχῆς μετὰ τοῦ σώματος θερμαντικὸν οἶνος, τὸ δὲ λεῖον καὶ διακριτικὸν ὄψεως διὰ ταῦτά τε ἰδεῖν λαμπρὸν καὶ στίλβον λιπαρόν τε φανταζόμενον ἐλαιηρὸν εἶδος, πίττα καὶ κίκι καὶ ἔλαιον αὐτὸ ὅσα τʼ ἄλλα τῆς αὐτῆς δυνάμεως· ὅσον δὲ διαχυτικὸν μέχρι φύσεως τῶν περὶ τὸ στόμα συνόδων, ταύτῃ τῇ δυνάμει γλυκύτητα παρεχόμενον, μέλι τὸ κατὰ πάντων μάλιστα πρόσρημα ἔσχεν, τὸ δὲ τῆς σαρκὸς διαλυτικὸν τῷ κάειν, ἀφρῶδες γένος, ἐκ πάντων ἀφορισθὲν τῶν χυμῶν, ὀπὸς ἐπωνομάσθη.
60b. and all that kind which tends to expand the contracted parts of the mouth, so far as their nature allows, and by this property produces sweetness, has received as a general designation the name of “honey”; and the foamy kind, which tends to dissolve the flesh by burning, and is secreted from all the saps, is named “verjuice.” Of the species of earth, that which is strained through water becomes a stony substance in the following way. When the water commingled therewith is divided in the process of mingling, it changes into the form of air; and when it has become air it rushes up to its own region; but because there was no void space above them, therefore it pressed against the adjacent air; and it, being heavy, when pressed and poured round the mass of earth, crushed it forcibly and compressed it into the spaces from which the new air was ascending. But when earth is thus compressed by the air so as to be indissoluble by water it forms “stone”; of which the fairer sort is that composed of equal and uniform parts and transparent, and the coarser sort the opposite. That kind from which all the moisture has been carried off by the rapidity of fire, and which is more brittle in its composition than the first kind, is the kind to which we have given the name of “earthenware.”
60b. γῆς δὲ εἴδη, τὸ μὲν ἠθημένον διὰ ὕδατος τοιῷδε τρόπῳ γίγνεται σῶμα λίθινον. τὸ συμμιγὲς ὕδωρ ὅταν ἐν τῇ συμμείξει κοπῇ, μετέβαλεν εἰς ἀέρος ἰδέαν· γενόμενος δὲ ἀὴρ εἰς τὸν ἑαυτοῦ τόπον ἀναθεῖ. κενὸν δʼ ὑπερεῖχεν αὐτῶν οὐδέν· τὸν οὖν πλησίον ἔωσεν ἀέρα. ὁ δὲ ἅτε ὢν βαρύς, ὠσθεὶς καὶ περιχυθεὶς τῷ τῆς γῆς ὄγκῳ, σφόδρα ἔθλιψεν συνέωσέν τε αὐτὸν εἰς τὰς ἕδρας ὅθεν ἀνῄει ὁ νέος ἀήρ· συνωσθεῖσα δὲ ὑπὸ ἀέρος ἀλύτως ὕδατι γῆ συνίσταται πέτρα, καλλίων μὲν ἡ τῶν ἴσων καὶ ὁμαλῶν διαφανὴς μερῶν, αἰσχίων δὲ ἡ ἐναντία. τὸ δὲ ὑπὸ πυρὸς τάχους τὸ νοτερὸν πᾶν ἐξαρπασθὲν καὶ κραυρότερον ἐκείνου συστάν, ᾧ γένει κέραμον ἐπωνομάκαμεν, τοῦτο γέγονεν·
60d. But sometimes, when moisture is still left in the earth and it has been fused by fire and has cooled again, it forms the species which is black in hue. On the other hand there are two kinds, which, in exactly the same manner, are isolated after the mixture from much of their water, but are composed of finer parts of earth, and are saline: when these have become semi-solid and soluble again by water, one of them is purgative of oil and earth and forms the species called “lye”; and the other, which blends well with the combinations which affect the sensation of the mouth, is that substance which is customarily termed “beloved of the gods,” namely “salt.”
60d. ἔστιν δὲ ὅτε νοτίδος ὑπολειφθείσης χυτὴ γῆ γενομένη διὰ πυρὸς ὅταν ψυχθῇ, γίγνεται τὸ μέλαν χρῶμα ἔχον λίθος. τὼ δʼ αὖ κατὰ ταὐτὰ μὲν ταῦτα ἐκ συμμείξεως ὕδατος ἀπομονουμένω πολλοῦ, λεπτοτέρων δὲ ἐκ γῆς μερῶν ἁλμυρώ τε ὄντε, ἡμιπαγῆ γενομένω καὶ λυτὼ πάλιν ὑφʼ ὕδατος, τὸ μὲν ἐλαίου καὶ γῆς καθαρτικὸν γένος λίτρον, τὸ δʼ εὐάρμοστον ἐν ταῖς κοινωνίαις ταῖς περὶ τὴν τοῦ στόματος αἴσθησιν ἁλῶν κατὰ λόγον [νόμου] θεοφιλὲς σῶμα ἐγένετο.
60e. As regards the kinds which are a blend of these two, and are dissoluble by fire and not by water, their composition is due to the following cause. Fire and air do not melt masses of earth; for, inasmuch as their particles are smaller then the interstices of its structure, they have room to pass through without forcible effort and leave the earth undissolved, with the result that it remains unmelted; whereas the particles of water, being larger, must use force to make their way out, and consequently dissolve and melt the earth.
60e. τὰ δὲ κοινὰ ἐξ ἀμφοῖν ὕδατι μὲν οὐ λυτά, πυρὶ δέ, διὰ τὸ τοιόνδε οὕτω συμπήγνυται. γῆς ὄγκους πῦρ μὲν ἀήρ τε οὐ τήκει· τῆς γὰρ συστάσεως τῶν διακένων αὐτῆς σμικρομερέστερα πεφυκότα, διὰ πολλῆς εὐρυχωρίας ἰόντα, οὐ βιαζόμενα, ἄλυτον αὐτὴν ἐάσαντα ἄτηκτον παρέσχεν· τὰ δὲ ὕδατος ἐπειδὴ μείζω πέφυκεν μέρη, βίαιον ποιούμενα τὴν διέξοδον, λύοντα αὐτὴν τήκει. ΤΙ. γῆν μὲν γὰρ ἀσύστατον ὑπὸ βίας οὕτως ὕδωρ μόνον λύει, συνεστηκυῖαν δὲ πλὴν πυρὸς οὐδέν·
61a. Tim. Thus earth when it is not forcibly condensed is dissolved only by water; and when it is condensed it is dissolved by fire only, since no entrance is left for anything save fire. Water, again, when most forcibly massed together is dissolved by fire only, but when massed less forcibly both by fire and air, the latter acting by way of the interstices, and the former by way of the triangles; but air when forcibly condensed is dissolved by nothing save by way of its elemental triangles, and when unforced it is melted down by fire only. As regards the classes of bodies which are compounds of earth and water, so long as the water occupies the interspaces of earth which are forcibly contracted, the portions of water which approach from without find no entrance, but flow round the whole mass and leave it undissolved.
61a. εἴσοδος γὰρ οὐδενὶ πλὴν πυρὶ λέλειπται. τὴν δὲ ὕδατος αὖ σύνοδον τὴν μὲν βιαιοτάτην πῦρ μόνον, τὴν δὲ ἀσθενεστέραν ἀμφότερα, πῦρ τε καὶ ἀήρ, διαχεῖτον, ὁ μὲν κατὰ τὰ διάκενα, τὸ δὲ καὶ κατὰ τὰ τρίγωνα· βίᾳ δὲ ἀέρα συστάντα οὐδὲν λύει πλὴν κατὰ τὸ στοιχεῖον, ἀβίαστον δὲ κατατήκει μόνον πῦρ. τὰ δὴ τῶν συμμείκτων ἐκ γῆς τε καὶ ὕδατος σωμάτων, μέχριπερ ἂν ὕδωρ αὐτοῦ τὰ τῆς γῆς διάκενα καὶ βίᾳ συμπεπιλημένα κατέχῃ, τὰ μὲν ὕδατος ἐπιόντα ἔξωθεν εἴσοδον οὐκ ἔχοντα μέρη περιρρέοντα τὸν ὅλον ὄγκον ἄτηκτον εἴασεν, τὰ δὲ πυρὸς εἰς τὰ τῶν ὑδάτων διάκενα εἰσιόντα, ὅπερ ὕδωρ γῆν, τοῦτο πῦρ [ἀέρα] ἀπεργαζόμενα, τηχθέντι τῷ κοινῷ σώματι ῥεῖν μόνα αἴτια συμβέβηκεν·
61b. But when portions of fire enter into the interspaces of the water they produce the same effects on water as water does on earth; consequently, they are the sole causes why the compound substance is dissolved and flows. And of these substances those which contain less water than earth form the whole kind known as “glass,” and all the species of stone called “fusible”; while those which contain more water include all the solidified substances of the type of wax and frankincense.
61b. τυγχάνει δὲ ταῦτα ὄντα, τὰ μὲν ἔλαττον ἔχοντα ὕδατος ἢ γῆς, τό τε περὶ τὴν ὕαλον γένος ἅπαν ὅσα τε λίθων χυτὰ εἴδη καλεῖται, τὰ δὲ πλέον ὕδατος αὖ, πάντα ὅσα κηροειδῆ καὶ θυμιατικὰ σώματα συμπήγνυται.
61c. And now we have explained with some fullness the Four Kinds, which are thus variegated in their shapes and combinations and permutations; but we have still to try to elucidate the Causes which account for their affective qualities. Now, first of all, the quality of sense-perceptibility must always belong to the objects under discussion; but we have not as yet described the generation of flesh and the appurtenances of flesh, nor of that portion of Soul which is mortal. But, in truth, these last cannot be adequately explained apart from the subject of the sensible affections, nor the latter without the former; while to explain both simultaneously is hardly possible.
61c. καὶ τὰ μὲν δὴ σχήμασι κοινωνίαις τε καὶ μεταλλαγαῖς εἰς ἄλληλα πεποικιλμένα εἴδη σχεδὸν ἐπιδέδεικται· τὰ δὲ παθήματα αὐτῶν διʼ ἃς αἰτίας γέγονεν πειρατέον ἐμφανίζειν. πρῶτον μὲν οὖν ὑπάρχειν αἴσθησιν δεῖ τοῖς λεγομένοις ἀεί, σαρκὸς δὲ καὶ τῶν περὶ σάρκα γένεσιν, ψυχῆς τε ὅσον θνητόν, οὔπω διεληλύθαμεν· τυγχάνει δὲ οὔτε ταῦτα χωρὶς τῶν περὶ τὰ παθήματα ὅσα αἰσθητικὰ οὔτʼ ἐκεῖνα ἄνευ τούτων δυνατὰ ἱκανῶς λεχθῆναι, τὸ δὲ ἅμα σχεδὸν οὐ δυνατόν.
61d. Therefore, we must assume one of the two, to begin with, and return later to discuss our assumptions. In order, then, that the affective properties may be treated next after the kinds, let us presuppose the facts about body and soul. Firstly, then, let us consider how it is that we call fire “hot” by noticing the way it acts upon our bodies by dividing and cutting.
61d. ὑποθετέον δὴ πρότερον θάτερα, τὰ δʼ ὑποτεθέντα ἐπάνιμεν αὖθις. ἵνα οὖν ἑξῆς τὰ παθήματα λέγηται τοῖς γένεσιν, ἔστω πρότερα ἡμῖν τὰ περὶ σῶμα καὶ ψυχὴν ὄντα. πρῶτον μὲν οὖν ᾗ πῦρ θερμὸν λέγομεν, ἴδωμεν ὧδε σκοποῦντες, τὴν διάκρισιν καὶ τομὴν αὐτοῦ περὶ τὸ σῶμα ἡμῶν γιγνομένην ἐννοηθέντες.