Bibliotheca Polyglotta

(τὰ τέσσαρα γένη) 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· 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 κατ’ 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 καθ’ ὅλον στασιμωτέρως ἐξ ἀνάγκης βέβηκεν. διὸ γῇ μὲν τοῦτο ἀπονέμοντες τὸν εἰκότα λόγον διασῴζομεν, ὕδατι δ’ αὖτῶν λοιπῶν τὸ δυσκινητότατον εἶδος, τὸ δ’ εὐκινητότατον πυρί, τὸ δὲ μέσον ἀέρι· καὶ τὸ μὲν σμικρότατον σῶμα πυρί, τὸ δ’ αὖ μέγιστον ὕδατι, τὸ δὲ μέσον ἀέρι· καὶ τὸ μὲν ὀξύτατον αὖ πυρί, τὸ δὲ δεύτερον ἀέρι, τὸ δὲ τρίτον ὕδατι. ταῦτ’ 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· τὸ δὲ δεύτερον δευτέρως τὰ αὐτὰ ταῦτ’ 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 καθ’ ἓν ἕκαστον μὲν τοῦ γένους ἑκάστου διὰ σμικρότητα οὐδὲν ὁρώμενον ὑφ’ ἡμῶν, συναθροισθέντων δὲ πολλῶν τοὺς ὄγκους αὐτῶν ὁρᾶσθαι· 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 δι’ ἀκριβείας ἀποτελεσθεισῶν ὑπ’ αὐτοῦ συνηρμόσθαι ταῦτα ἀνὰ λόγον. Ἐκ δὴ πάντων ὧνπερ τὰ γένη προειρήκαμεν ὧδ’ ἂν κατὰ τὸ εἰκὸς μάλιστ’ ἂν ἔχοι. γῆ μὲν συντυγχάνουσα πυρὶ διαλυθεῖσά τε ὑπὸ τῆς ὀξύτητος αὐτοῦ φέροιτ’ ἄν, εἴτ’ ἐν αὐτῷ πυρὶ λυθεῖσα εἴτ’ ἐν ἀέρος εἴτ’ ἐν ὕδατος ὄγκῳ τύχοι, μέχριπερ ἂν αὐτῆς πῃ συντυχόντα τὰ μέρη, πάλιν συναρμοσθέντα αὐτὰ αὑτοῖς, γῆ γένοιτο - οὐ γὰρ εἰς ἄλλο γε εἶδος ἔλθοι ποτ’ ἄν - ὕδωρ δὲ ὑπὸ πυρὸς μερισθέν, εἴτε καὶ ὑπ’ ἀέρος, ἐγχωρεῖ γίγνεσθαι συστάντα ἓν μὲν πυρὸς σῶμα, δύο δὲ ἀέρος· τὰ δὲ ἀέρος τμήματα ἐξ ἑνὸς μέρους διαλυθέντος δύ’ 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. ὧδε γὰρ δὴ λογισώμεθα αὐτὰ πάλιν, ὡς ὅταν ἐν πυρὶ λαμβανόμενον τῶν ἄλλων ὑπ’ 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 δ’ ἂν εἰς ἄλλο τι γιγνόμενον ἧττον ὂν κρείττονι μάχηται, λυόμενον οὐ παύεται. 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 δ’ 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 δ’ ἐν τοῖς εἴδεσιν αὐτῶν ἕτερα ἐμπεφυκέναι γένη τὴν ἑκατέρου τῶν στοιχείων αἰτιατέον σύστασιν, μὴ μόνον ἓν ἑκατέραν μέγεθος ἔχον τὸ τρίγωνον φυτεῦσαι κατ’ ἀρχάς, ἀλλ’ ἐλάττω τε καὶ μείζω, τὸν ἀριθμὸν δὲ ἔχοντα τοσοῦτον ὅσαπερ ἂν ᾖ τἀν τοῖς εἴδεσι γένη. 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.

Sed haec dimittenda sunt. Et iam genera quatuor a nobis paulo ante digesta, in (25) ignem, terram, aquam, aeremque distribuamus. Terrae cubicam speciem assignemus. Nam (26) omnium quatuor maxime immobilis terra est, et corporalium omnium conpacta maxime. Tale (27) vero illud praecipue factum esse necessaruim est, quod firmissimas tutissimasque possidet ba(28)ses. In triangulis porro a principio positis, qui aequilateres sunt, firmiorem tutioremque (29) quam inaequilateres basem possident. Et quod ex utroque compositum est planum ae(30)quilatere aequilateri quadrungulum, certe triangulo tam quo ad totum quam quoad partes (31) stabilius necessario provenit. Quamobrem si convenientem probabilemque sequi ratio(32)nem velimus, terrae id tribuamus: Aquae deinde, quod tribus reliquis est immobili(33)us: igni quod mobilissimum: Aeri medium. Et corpus quidem minimum igni, aquae (34) maximum, aeri medium: acutissimum quoque igni, secundum ab hoc aeri, aquae terti(35)um. Ex his omnibus quod bases paucissimas habet, velocissimum esse necessarium est. Est (36) enim ad penetrandum promptissimum, quippe cum prorsus sit omnium acutissimum. Le(37)vissimum quoque, cum ex paucissimis partibus eisdem constet. Quod secundum est, se(38)cundo loco habeat haec oportet. Tertio tertium. Igitur secundum rectam probabilemque(39) rationem pyramidis species solida elementum semenque sit ignis. Secundam vero generati(40)one speciem aeri, aquae tertiam tribuamus. De his omnibus adeo parvis ita putandum est, (41) quod si singula duntaxat singulorum generum capiantur, nullum eorum propterparvita(42)tem cerni a nobis poterit: sin multa invicem congregentur, eorum moles magnitudinesque (43) cernentur. Quin etiam haec omnia, adeo tanta ubique quoad multitudines, motus, atque po(44)tentias proportione exacte absoluta connexaque sunt, quantam necessitatis natura libens (45) et persuasa capere poterat. Ex omnibus sane quorum genera supra narravimus, ita meri(46)to se res habere videtur. Terra cum in ignem inciderit, eius acumine dissoluta fertur reso(47)luta in ignem, aut aerem, aut aquam, quousque partes ipsius congressae iterum, sibique invicem (48) copulatae terram reficiant. Non enim in aliam unquam speciem transmigraret. Aqua prae(49)terea ab igni vel divisa in partes, unum, partibus suis reconciliatis, ignis corpus, ae(50)ris duo facit: portiones vero aeris ex una dissoluta parte duo ignis corpora faciunt. Rur(51)sus quando ignis ab aere vel aqua vel terra aliqua occupatur, et ipse quidem paucus in (52) multis movetur, atque in agitatis pugnat, iactatusque distrahitur, duo corpora ignis in specie(53)em aeris unam concrescunt: deinde superato aere atque disperso, ex totis duobus atque di(54)midio una aquae tota species coalescit. Denique sic ea rursus confideremus. quoties ab igne (1) comprehensum aliorum genus aliquod angulorum laterumque ipsius acumine scindi(2)tur, tum demum discerpi definit cum in ignis naturam transierit. Simile enim idemque ge(3)nus quodlibet a simili eodemque minime patitur: quousque vero in aliud permutatur, im(4)becilliusque cum potentiore luctatur, disolvi non definit. Rursus quando minora a multis (5) maioribus circumventa sunt, et pauca lacerata extinguuntur, cum in vincentis ideam con(6)stitui velint, cessant extingui, sitque ex igni aer, ex aere aqua. Quodsi in haec transitus fu(7)erit, et aliorum aliquod genus impugnet, non cessant agitata dissolvi priusquam aut om(8)nino cum dissolubilia sint depulsa ad cognatum refugiant, aut expugnata in unum quid(9)dam, ex multis superanti simile tandem evadant, familiariterque cum victore permaneant. (10) Enimvero per has passiones sedes vicissim cuncta commutant. Generis namque cuius(11)libet multitudines per locum proprium distinguuntur, ob sedis ipsius agitationem. Quae (12) vero dissimilia invicem facta sunt, propter fluctum concussionemque ad locum eorum (13) quibus similia evasere, feruntur. Corpora igitur immixta ac prima ex causis huiusmo(14)di fabricata sunt. Quod autem in eorum speciebus alia quoque innata sunt genera, cau(15)sa est elementi utriusque constitutio: quae non solum ab initio unum cum magnitudine (16) triangulum peperit, sed etiam maiora et minora tot quidem numero, quot in speciebus (17) sunt genera. Quapropter mixta haec in seipsis atque invicem, infinitam habent varieta(18)tem: cuius peritos esse eos oportet qui de natura sunt rationem probabilem reddituri.

But, leaving this enquiry, let us proceed to distribute the elementary forms, which have now been created in idea, among the four elements. We have now to assign to the four elements their respective forms,—to earth the cube, to water the icosahedron, to air the octahedron, to fire the pyramid. Individual particles cannot be seen: masses of each kind are visible. To earth, then, let us assign the cubical form; for earth is the most immoveable of the four and the most plastic of all bodies, and that which has the most stable bases must of necessity be of such a nature. Now, of the triangles which we assumed at first, that which has two equal sides is by nature more firmly based than that which has unequal sides; and of the compound figures which are formed out of either, the plane equilateral quadrangle has necessarily a more stable basis than the equilateral triangle, both in the whole and in the parts. Wherefore, in assigning this figure to earth, we adhere to probability; and to water we assign that one of the remaining forms which is the least moveable; and the most moveable of them to fire; and to air that which is intermediate. Also we assign the smallest body to fire, and the greatest to water, and the intermediate in size to air; and, again, the acutest body to fire, and the next in acuteness to air, and the third to water. Of all these elements, that which has the fewest bases must necessarily be the most moveable, for it must be the acutest and most penetrating in every way, and also the lightest as being composed of the smallest number of similar particles: and the second body has similar properties in a second degree, and the third body in the third degree. and let us assign the element which was next in the order of generation to air, and the third to water. We must imagine all these to be so small that no single particle of any of the four kinds is seen by us on account of their smallness: but when many of them are collected together their aggregates are seen. And the ratios of their numbers, motions, and other properties, everywhere God, as far as necessity allowed or gave consent, has exactly perfected, and harmonized in due proportion. [Of the three elements, fire, air, water, a denser, if overpowered by a rarer, is forced to change into a rarer, and vice versa. Earth, however, which is the densest of all, cannot change, because its component triangles are unlike those of the other elements. Change of nature is accompanied by change of place.] From all that we have just been saying about the elements or kinds, the most probable conclusion is as follows: —earth, when meeting with fire and dissolved by its sharpness, whether the dissolution take place in the fire itself or perhaps in some mass of air or water, is borne hither and thither, until its parts, meeting together and mutually harmonizing, again become earth; for they can never take any other form. But water, when divided by fire or by air, on re-forming, may become one part fire and two parts air; and a single volume of air divided becomes two of fire. Again, when a small body of fire is contained in a larger body of air or water or earth, and both are moving, and the fire struggling is overcome and broken up, then two volumes of fire form one volume of air; and when air is overcome and cut up into small pieces, two and a half parts of air are condensed into one part of water. Let us consider the matter in another way. When one of the other elements is fastened upon by fire, and is cut by the sharpness of its angles and sides, it coalesces with the fire, and then ceases to be cut by them any longer. For no element which is one and the same with itself can be changed by or change another of the same kind and in the same state. But so long as in the process of transition the weaker is fighting against the stronger, the dissolution continues. Again, when a few small particles, enclosed in many larger ones, are in process of decomposition and extinction, they only cease from their tendency to extinction when they consent to pass into the conquering nature, and fire becomes air and air water. But if bodies of another kind go and attack them [i. e. the small particles], the latter continue to be dissolved until, being completely forced back and dispersed, they make their escape to their own kindred, or else, being overcome and assimilated to the conquering power, they remain where they are and dwell with their victors, and from being many become one. And owing to these affections, all things are changing their place, for by the motion of the receiving vessel the bulk of each class is distributed into its proper place; but those things which become unlike themselves and like other things, are hurried by the shaking into the place of the things to which they grow like. [The varieties of the four elements are due to differences in the size of the elementary triangles.] Now all unmixed and primary bodies are produced by such causes as these. As to the subordinate species which are included in the greater kinds, they are to be attributed to the varieties in the structure of the two original triangles. For either structure did not originally produce the triangle of one size only, but some larger and some smaller, and there are as many sizes as there are species of the four elements. Hence when they are mingled with themselves and with one another there is an endless variety of them, which those who would arrive at the probable truth of nature ought duly to consider.

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