Propter quid igitur non totius caeli corpus tale? Quia necesse manere aliquid corporis lati circum quod in medio; huius autem nullam possibile est manere partem, neque universaliter neque in medio. Etenim si secundum naturam motus erit ipsius ad medium, natura autem circummovetur, non utique esset sempiternus motus. Nihil enim praeter naturam sempiternum: posterius autem quod praeter naturam eo quod secundum naturam; et excessus quidam est in generatione quod praeter naturam, eius quod secundum naturam. Necesse igitur terram esse: hoc enim quiescit in medio. Nunc quidem igitur supponatur hoc, posterius autem demonstrabitur de ipso. 251 Why, then, is not the whole body of the heaven of the same character as that part? Because there must be something at rest at the center of the revolving body; and of that body no part can be at rest, either elsewhere or at the center. It could do so only if the body's natural movement were towards the center. But the circular movement is natural, since otherwise it could not be eternal: for nothing unnatural is eternal. The unnatural is subsequent to the natural, being a derangement of the natural which occurs in the course of its generation. Earth then has to exist; for it is earth which is at rest at the center. (At present we may take this for granted: it shall be explained later.) Sed adhuc, si terram, necesse et ignem esse. 252 But if earth must exist, so must fire. Contrariorum enim si alterum natura, necesse et alterum esse natura: si vero sit contrarium, et esse quandam ipsius naturam: eadem enim materia contrariorum. 253 For, if one of a pair of contraries naturally exists, the other, if it is really contrary, exists also naturally. In some form it must be present, since the matter of contraries is the same. Et privatione prius affirmatio, dico autem puta calidum frigido: quies autem et gravitas dicuntur per privalionem levitatis et motus. 254 Also, the positive is prior to its privation (warm, for instance, to cold), and rest and heaviness stand for the privation of lightness and movement. Sed adhuc, si quidem est ignis et terra, necesse et intermedia ipsorum esse corpora: contrarietatem enim habet unumquodque ad unumquodque elementorum. Supponatur autem et hoc nunc, posterius autem tentandum ostendere. 255 But further, if fire and earth exist, the intermediate bodies must exist also: each element stands in a contrary relation to every other. (This, again, we will here take for granted and try later to explain.) His autem existentibus, manifestum quoniam necesse est generationem esse, eo quod nullum ipsorum possibile est esse sempiternum: patiuntur enim et agunt contraria ab invicem, et corruptiva invicem sunt. 256 [Since this is so, in] these four elements generation clearly is involved, since none of them can be eternal: for contraries interact with one another and destroy one another. Adhuc autem non rationabile est esse aliquod mobile sempiternum, cuius non contingit esse secundum naturam motum sempiternum: horum autem est motus. Quod quidem igitur necessarium esse generationem, ex his manifestum. 257 Further, it is inconceivable that a movable body should be eternal, if its movement cannot be regarded as naturally eternal: and these bodies we know to possess movement. Thus we see that generation is necessarily involved. Si autem generationem, necessarium et aliam esse lationem, aut unam aut plures: secundum enim eam quae totius, similiter necessarium habere et elementa corporum ad invicem. Dicetur autem et de hoc in sequentibus planius. 258 But if so, there must be at least one other circular motion: for a single movement of the whole heaven would necessitate an identical relation of the elements of bodies to one another. This matter also shall be cleared up in what follows: Nunc autem tantum manifestum est, propter quam causam plura sunt circularia corpora: quia necesse generationem esse; generationem autem si quidem et ignem; hunc autem et alia si quidem et terram; hanc autem quia manere necesse est aliquid semper, si quidem moveri aliquid semper. 259 But for the present so much is clear, that the reason why there is more than one circular body is the necessity of generation, which follows on the presence of fire, which, with that of the other bodies, follows on that of earth; and earth is required because eternal movement in one body necessitates eternal rest in another. 330. Postquam Philosophus determinavit de diversitate partium situalium caeli, hic determinat de diversitate partium quantum ad ordinem sphaerarum, ostendens videlicet causam quare in caelo non est una sphaera tantum circulariter mota, sed sunt plures sphaerae quae circulariter moventur. Et circa hoc tria facit: 330. After discussing the diversity of positional parts of the heaven, the Philosopher here settles the question of the diversity of parts based on the order of the spheres, and explains why there is not just one circularly-moved sphere in the heaven but several of them. Concerning this he does three things: primo ponit dubitationem; first he states the problem; secundo ostendit difficultatem solutionis, ibi: et quidem a longe tentantibus etc.; secondly, he explains why this problem is difficult to solve, at though we have to pursue 332; tertio incipit solvere, ibi: unumquodque est quorum est opus et cetera. thirdly, he begins to solve it, at the reason must be sought 333. 331. Circa primum considerandum est quod, si contingeret motus circulares esse contrarios, non esset difficile videre quare in caelo non est tantum unus motus circularis, sed plures. Cum enim contraria differant specie, eo quod contrarietas est differentia secundum formam, ut dicitur X Metaphys., non esset universum perfectum in suis speciebus, si esset unus motus contrarius et non alius, puta si esset motus deorsum et non esset motus sursum. Quia ergo, ut supra probatum est, unus motus circularis non est contrarius alteri, oportet diligenter considerare quae est necessitas quod in caelo essent multi et diversi motus circulares. Et quaestio satis congrue sequitur ad praemissa, in quibus dictum est quod sursum et deorsum et alia huiusmodi aliter considerantur in caelo quantum ad primum motum, et aliter quantum ad secundum. 331. In regard to the first it should be kept in mind that if circular motions were contrary, it would not be difficult to see why there are many circular motions in the heaven and not just one. For since contraries differ specifically, inasmuch as contrariety is a difference with respect to form, as is said in Metaphysics X, the universe would not be perfect in its species if there were one contrary motion and not another, for example, if there were downward motion and not upward motion. Since, therefore, it has been previously proved that one circular motion is not contrary to another, we should inquire diligently as to the necessity of having many and diverse circular motions in the heaven. This question quite logically follows our previous discussion where it was said that up and down, and other such are assigned to the heaven in one way with respect to the first motion, and in another way with respect to the second. 332. Deinde cum dicit: et quidem a longe tentantibus etc., ostendit difficultatem solvendae quaestionis. Hoc enim dicit esse considerandum hominibus qui tentant facere quaestionem a longe, idest de corporibus caelestibus longe a nobis existentibus; cum tamen de his quae sunt elongata a nobis, non possimus habere certum iudicium. Corpora autem caelestia non ita sunt longe a nobis tanto, idest secundum quantitatem localis distantiae; sed multo magis eo quod pauca accidentium eorum cadant sub sensum nostrum; cum tamen connaturale sit nobis quod ex accidentibus, idest sensibilibus, deveniamus ad cognoscendam naturam alicuius rei. Hanc autem elongationem dicit multo maiorem esse quam localem: quia si consideremus localem distantiam, aliqua proportio est distantiae qua distat a nobis corpus caeleste, ad distantiam qua distat a nobis aliquod inferiorum corporum, puta lapis aut lignum, et utraque distantia est unius generis; sed accidentia caelestium corporum sunt alterius rationis, et omnino improportionata accidentibus inferiorum corporum. Et tamen, quamvis sit difficile, dicamus propter quid est talis diversitas motus in caelo. Et huius diversitatis causa est accipienda ex his quae nunc dicentur. 332. Then, at though we have to pursue [249], he points out the difficulty of solving this question. For that is difficult for men to consider when the question is from afar, i.e., concerning the heavenly bodies far removed from us, since concerning things distant from us we cannot have a certain judgment. However, heavenly bodies are not only removed by so much, i.e., according to the quantity of local distance, but much more by the fact that few of their accidents fall on our sense observation, whereas it is connatural for us to pass from the knowledge of accidents, i.e., sensible things, to an understanding of a thing's nature. He states this distance to be much more than the local distance. For if we should consider the local distance, there is some proportion between the distance separating us from a heavenly body and that separating us from various lower bodies, e.g., a stone or some wood, and both distances are in one genus, but the accidents of heavenly bodies have a different notion and are wholly improportionate to the accidents of lower bodies. Yet, in spite of the difficulty, let us inquire into the "why" of the variety of heavenly motions. And the cause of this variety will be derived from what we are about to say. 333. Deinde cum dicit: unumquodque est quorum est opus etc., assignat causam praedictorum. 333. Then, at the reason must be sought [250], he assigns the cause of the aforesaid. Et primo assignat eam per viam compositionis, procedendo a primo ad ultimum quod quaeritur; First he assigns it by the method of composition [synthesis], going from what is first to what is last in the order of inquiry; secundo per viam resolutionis, procedendo ab ultimo quod quaeritur usque ad primum, ibi: nunc autem tantum manifestum est et cetera. secondly, by that of resolution [analysis], proceeding from what is last sought to what is first, at but for the present 343. Circa primum ponit talem rationem. Si caelum est quoddam corpus divinum, necesse est motum eius esse sempiternum et circularem; si motus eius est sempiternus et circularis, necesse est terram esse; si terra est, necesse est ignem esse; si ignis est et terra, est necesse etiam aliqua corpora intermedia esse; si autem sunt huiusmodi corpora, necesse est generationem esse; si autem generatio est, necesse est plures motus esse in caelo. Ergo, si caelum est corpus perpetuum et divinum, necesse est plures motus esse in caelo, et per consequens plura corpora mobilia. With respect to the first [250] he gives the following argument: If the heaven is a certain divine body, its motion must be eternal and circular; if its motion is eternal and circular, earth must exist; if earth exists, fire must exist; if fire and earth exist, there must be intermediate bodies; if such bodies exist, there must be generation; if there is generation there must be several motions in the heaven. Therefore, if the heaven is a perpetual and divine body, there must be a number of motions in the heaven, and consequently a number of mobile bodies. 334. Singula igitur per ordinem manifestat: et primo primum. Circa quod considerandum est quod Platonici ponebant unum Deum summum, qui est ipsa essentia bonitatis et unitatis, sub quo ponebant ordinem superiorum intellectuum separatorum, qui apud nos consueverunt intelligentiae vocari; et sub hoc ordine ponebant ordinem animarum, sub quo ordine ponebant ordinem corporum. Dicebant ergo quod inter intellectus separatos, superiores et primi dicuntur intellectus divini, propter similitudinem et propinquitatem ad Deum; alii vero non sunt divini, propter distantiam ad Deum; sicut etiam animarum supremae sunt intellectivae, infimae autem non intellectivae, sed irrationales. Corporum autem suprema et nobiliora dicebant esse animata, alia vero inanimata. Rursus dicebant quod supremae animae propter hoc quod dependent ex intelligentiis divinis, sunt animae divinae; et iterum corpora suprema, propter hoc quod sunt coniuncta animabus divinis, sunt corpora divina. 334. Then he explains each of these conditionals in order: and first of all the first one. With respect to this it must be remembered that the Platonists posited one supreme God Who is the very essence of goodness and unity, under Whom they put a superior order of separated intellects, which we are accustomed to call "intelligences"; under this order they placed the order of souls, and under this the order of bodies. They said, therefore, that among the separated intellects the first and superior ones are called "divine" intellects on account of their likeness and nearness to God; but the others are not 'divine, because of their distance from God. Similarly, among souls the supreme are intellective, while the lowest are not intellectual but irrational. The supreme and nobler bodies were said to be animate; the others inanimate. Furthermore, they said that the supreme souls, because they depend on the divine intelligences, were divine souls; and the supreme bodies, because united to divine souls, divine bodies. Hoc igitur modo etiam Aristoteles hic loquitur, dicens quod unumquodque quod habet propriam operationem, est propter suam operationem: quaelibet enim res appetit suam perfectionem sicut suum finem, operatio autem est ultima rei perfectio (vel saltem ipsum operatum, in his in quibus est aliquod opus praeter operationem, ut dicitur in I Ethic.); dictum est enim in II De anima quod forma est actus primus, operatio autem est actus secundus, tanquam perfectio et finis operantis. Et hoc est verum tam in corporalibus quam in spiritualibus, puta in habitibus animae; et tam in naturalibus quam in artificialibus. Dicit tamen quorum opus est, propter ea quae sunt contra naturam, sicut sunt monstra; quorum non est aliquod opus inquantum huiusmodi, sed patiuntur defectum operativae virtutis, ut patet in his qui nascuntur claudi vel caeci; non enim claudicatio est finis intentus a natura, propter quem faciat nasci animal claudum, sed hoc accidit praeter intentionem naturae ex defectu naturalium principiorum. Now, Aristotle uses this manner of speaking here. He says that anything which possesses its on operation exists for its operation, for everything seeks its perfection as its end; but operation is the ultimate perfection of a thing (or at least the product of the operation is, in the case of those things in which there is some product beyond the operation, as is said in Ethics I). For it is said in On the Soul II that form is first act, and operation second act as the perfection and end of the thing acting. And this is true both in material and in spiritual things (such as habits existing in the soul), and in natural as well as artificial things. And he adds the expression, "which produce a work" to take care of things contrary to nature, such as monstrosities, which produce no work as such, but suffer a defect in their operational power, as is plain in those born lame or blind. For lameness is not an end intended by nature, for the sake of which it makes an animal to be born lame; such a thing happens outside the intent of nature, by reason of a defect in the natural principles. Subdit autem quod operatio Dei est immortalitas. Nominat autem hic Deum, non solum primam causam omnium rerum, sed, more Platonicorum et aliorum gentilium, omnia quae dicuntur divina, secundum morem praedictum. Sed videtur quod immortalitas non sit operatio, sed potius differentia vel impassibilitas, sicut mortale est differentia vel passio. Dicendum est ergo quod immortalitas signat vitam indeficientem: vivere autem non solum nominat ipsum esse viventis, sed etiam operationem vitae, sicut intelligere est quoddam vivere, et sentire et alia huiusmodi, ut patet in II De anima et in IX Ethic. Et ad hoc exprimendum subiungit, haec autem, scilicet immortalitas, est vita sempiterna: propter quod etiam non dicit quod Dei operatio sit incorruptibilitas, quae importat solum sempiternitatem ipsius esse, sed dicit immortalitas, ut includat sempiternitatem operationis. Unde concludit quod, si aliquid mobilium dicatur Deus secundum modum praedictum, quod motus eius sit sempiternus; sicut et si qua substantia immobilis Deus dicitur, eius operatio est sempiterna absque motu; alioquin frustra esset talis res sempiterna non habens operationem sempiternam, propter quam unaquaeque res est. He adds further that God's operation is immortality, where "God" refers not only to the first cause of all things but to all things called "divine" according to the custom of the Platonists and other gentiles. But immortality appears not to be an operation but rather a difference or an impassibility. To this it must be answered that immortality designates unfailing life. Now life refers not only to the existence of the living being, but to its operation as well, as understanding is a certain living and as are sensing and other such, as is plain from On the Soul II and Ethics IX. This point is brought out when he says further that this, namely, immortality, is eternal life—for which reason he does not say that God's operation is indestructibility, which refers only to the eternity of His existence but he says it is immortality, in order to include eternity of action. Hence he concludes that if any mobile being is called "God" in this sense, its motion is eternal; just as, if some immobile substance is called "God," its operation is eternal without motion. If this were not so, then such a thing, eternal in existence but lacking an eternal operation (since things exist in order to act) would exist without a purpose. Quia ergo caelum est tale quod secundum antiquos Deus dicebatur, non quia sit ipse summus Deus, sed quia corpus eius est quoddam divinum, propter hoc quod est ingenitum et incorruptibile, ut supra ostensum est; inde est quod habet corpus circulare, ad hoc quod possit semper et circulariter moveri. Ostensum est enim in VIII Physic. quod solus motus circularis potest esse perpetuus: nam super lineam rectam infinitam nullus est motus, ut etiam in primo probatum est; super lineam autem rectam finitam non potest esse motus infinitus nisi per reflexionem, quae quidem non potest esse sine interpolatione quietis, ut probatur in VIII Physic. Therefore, since the heaven is such as to have been called "God" by the ancients, not indeed because it is the supreme God, but because its body is something divine by virtue of being ungenerated and indestructible, as was previously explained; consequently it possesses a circular body in order that it may be moved forever and in a circular way. For it has been shown in Physics VIII that only circular motion can be eternal, since there is no motion over an infinite straight line, as was also proved in Book I, and motion over a finite straight line cannot be infinite except by reflexion, which involves interposing states of rest, as was proved in Physics VIII. Et est attendendum quod Aristoteles hic probat sempiternitatem motus caeli ex sempiternitate corporis eius; qua via non fuit usus in VIII Physic., quia nondum probaverat sempiternitatem caeli. Sed quia ad motum caeli se habet ipsum corpus caeleste ut materia et subiectum, primum autem movens, scilicet Deus, sicut agens quod facit ipsum esse in actu; ex parte caeli probari potest quod sit potens semper moveri, ex parte autem voluntatis divinae dependet quod moveatur in actu vel semper vel non semper. It should be noted that Aristotle here proves the eternity of the motion of the heaven from the eternity of its body; but in Physics VIII he did not use this way, because he had not yet proved the eternity of the heaven. But because the heavenly body is related to the motion of the heaven as its matter and subject, whereas the first mover, namely, God, is the agent making it actually exist, then from the side of the heaven it can be preyed able to be moved forever, but on the part of the divine will depends whether it is to be actually moved forever or not forever. 335. Deinde cum dicit: propter quid igitur etc., ostendit secundam conditionalem, scilicet quod si caelum movetur sempiterno et circulari motu, quod necesse sit esse terram. Dicit ergo: si ita est quod caelum est corpus divinum sempiterne et circulariter motum, propter quid ergo non est tale corpus totius caeli, idest totius mundi, ut scilicet quaelibet pars mundi esset de natura caelestis corporis? 335. Then, at why, then, is not the whole body [251] he proves the second conditional, namely, that if the heaven is moved with an eternal and circular motion, earth must exist. He says, therefore: if it is true that the heaven is a divine body which is eternally and circularly moved, why then does not the entire heaven, i.e., the entire world, have such a body, i.e., why does not each part of the world have the nature of heavenly body? Et ad hoc respondet quod necesse est esse aliquid manens et quietum in medio corporis quod circulariter fertur: manifestum est enim quod omnis motus circularis est circa aliquod medium quiescens. Et hoc oportet esse aliquod corpus: nam hoc quod dico medium, non est aliquid subsistens, sed accidens alicui rei corporeae, si sit medium corporis. Non est autem possibile quod tale aliquid sit aliqua pars huius, idest aliqua pars caelestis corporis, quod supra dixerat corpus divinum, licet oporteat quod sit pars totius mundi. Et hoc probat dupliciter. To this he answers that there has to be something permanent and at rest in the middle [center] of the body which is in circular motion—for it is plain that every circular motion goes around something at rest. And this something must be a body: for the thing I am calling the middle [center] is not something subsistent, but an accident of a bodily thing, if it is the center of a body. Now such a thing cannot be a part of this, i.e., of the heavenly body, which has already been described as divine, although it must be a part of the whole world. This he proves in two ways. Primo quia nulla pars caelestis corporis universaliter potest quiescere ubicumque, cum corpori caelesti conveniat sempiternus motus, ut ostensum est: medium autem circa quod est motus circularis, oportet esse quietum. First, because no part of a heavenly body generally can be at rest everywhere, since to the heavenly body belongs eternal motion, as was shown. But the center about which there is circular motion must be stationary. Secundo quia specialiter non potest esse quod quiescat in medio. Quia si secundum naturam in medio quiesceret, naturaliter moveretur ad medium (unumquodque enim naturaliter movetur ad locum in quo quiescit, ut in primo habitum est): nulla autem pars corporis caeli naturaliter movetur ad medium, quia naturalis eius motus est quod moveatur circulariter, et, sicut in primo habitum est, unius simplicis corporis non possunt esse duo motus naturales. Secondly, because taken specifically it cannot rest in the center. For if it rested there naturally, it would be naturally moved to the center (for each thing is naturally moved to the place in which it rests naturally, as was explained in Book I). But no part of the heavenly body is naturally moved to the center, because its natural motion is for it to be moved circularly, and, as was explained in Book I, no simple body can possess two natural motions. Unde relinquitur quod quies partis illius caelestis corporis in medio esset ei contra naturam. Et ex hoc sequitur quod motus caeli non possit esse sempiternus: quia non potest esse nisi sit aliquid quietum in medio, et si quies eius quod est in medio esset violenta, sequeretur quod non posset esse sempiterna; et per consequens nec motus eius sempiternus. Nihil enim quod est praeter naturam, est sempiternum: quia illud quod est praeter naturam, est posterius eo quod est secundum naturam: quod quidem patet ex hoc quod in generatione cuiuslibet rei, id quod est praeter naturam est excessus quidam, idest corruptio et defectus, eius quod est secundum naturam (sicut videmus quod monstra sunt quaedam corruptiones et defectus rei naturalis); corruptio autem et defectus est naturaliter posterior, sicut privatio quam habitus. Non autem est possibile id quod est naturaliter prius, nunquam esse, et id quod est naturaliter posterius, esse semper. Unde patet quod non est possibile id quod est violentum esse sempiternum. Id autem quod in medio quiescit, sempiterne quiescit, sicut et caelum sempiterne movetur. Relinquitur ergo quod oporteat esse aliquid quod naturaliter quiescat in medio, si motus caeli est circularis et sempiternus. Hoc autem quod naturaliter quiescit in medio, est terra, ut infra ostendetur. Ergo, si caelum movetur circulariter et sempiterne, necesse est terram esse, quod fuit propositum. Hence it remains that the rest of a part of the heavenly body in the center would be against its nature. From this it follows that the motion of the heaven could not be eternal: because it cannot take place unless there is something at rest in the center, and if the state of rest of that of it which was in the center were violent, it would follow that it [the rest] could not be eternal, and consequently neither could the heaven's motion be eternal. For nothing contrary to nature is eternal—since what is contrary to nature is subsequent to what is according to nature. This is plain from the fact that in the generation of anything, whatever is outside nature is a kind of excess, i.e., a corruption and defect of that which is according to nature (for example, monstrosities are certain corruptions and defects of a natural thing). But corruptions and defect are naturally posterior, just as privation is subsequent to possession. Now it is not possible that something naturally prior should never exist, and that what is naturally apt to be later, should always exist. Consequently, it is plain that what is violent cannot be eternal. But that which is at rest in the center, is eternally at rest, just as the heaven is eternally in motion. What is left, therefore, is that there must be something naturally at rest in the center, if the motion of the heaven is circular and eternal. But it is the earth that is naturally at rest in the center, as will be proved later. Therefore, if the heaven is moved circularly and eternally, then earth must exist. And this is what was proposed to be proved. 336. Deinde cum dicit: sed adhuc si terram etc., ostendit tertiam conditionalem, scilicet quod si est terra, quod sit ignis. 336. Then, at but if earth must exist [252] he proves the third conditional, namely, if there is earth, there is fire. Et primo proponit quod intendit, dicens quod adhuc, si necesse est terram esse, necesse est et ignem esse. First he proposes what he intends, and says that it is also true that if earth must exist, then fire must exist. Secundo ibi: contrariorum enim etc., probat hoc duabus rationibus. Secondly, for, if one of a pair of contraries, he proves this with two arguments. Quarum prima talis est. Si unum contrariorum est in natura, necesse est etiam quod alterum sit in natura. Et hoc quidem probat sic: quia si sit aliquod contrariorum, necesse est quod sit aliqua natura ei subiecta, ut patet ex I Physic.; est autem eadem materia contrariorum, ut ibidem ostenditur, et sic oportet quod materia unius contrarii habeat potentiam ad aliud contrarium; quae quidem potentia esset frustra, si illud contrarium non posset esse in natura. Unde, cum nihil sit frustra in natura, necesse est quod si unum contrariorum est, quod et reliquum sit. Ignis autem et terra sunt contraria: quia maxime distant secundum contrarietatem situs, de qua nunc loquimur, inquantum unum est gravissimum et aliud levissimum (quantum autem ad alias qualitates, ignis maxime contrariatur aquae, sicut calidissimum frigidissimo: sed nunc loquitur de istis corporibus secundum eorum situm; sic enim sunt partes totius universi). Relinquitur ergo quod si est terra, necesse est etiam ignem esse. The first is this. If one contrary exists in nature, the other also must exist in nature. He proves this as follows: If there be any contrary, there must be a matter subject to it, as is plain from Physics I; but the matter of contraries is the same, as is shown in the same place. Consequently, the matter of one contrary must be in potency to the other. Now this potency would be in vain if that other contrary could not exist in nature. But since nothing is in vain in nature, then, if one contrary exists, so must the other. Now fire and earth are contraries, for they are the maximum distance apart, so far as contrariety of position is concerned, inasmuch as one is the heaviest of all things and the other the lightest (although in respect of other qualities, fire is especially contrary to water, as the hottest to the coldest—however, we are now speaking of bodies from the viewpoint of position, from which aspect they are parts of the whole universe). Consequently, if there is earth, there must also be fire. 337. Secundam rationem ponit ibi: et privatione et cetera. Circa quam considerandum est quod semper contraria se habent secundum peius et melius, ut dicitur in I Physic.; ita scilicet quod unum est privatio et defectus respectu alterius, sicut frigidum respectu calidi, et nigrum respectu albi. Manifestum est autem quod affirmatio, idest omne quod positive dicitur ut aliquid completum, est prius eo quod dicitur per privationem et defectum, sicut calidum est prius frigido. Quies autem et gravitas, quae attribuuntur terrae, dicuntur per privationem levitatis et motus, quae attribuuntur igni: ergo ignis naturaliter est prior terra. Posito autem posteriori, ponitur prius. Ergo necesse est quod si est terra, quod sit ignis. Et est considerandum quod Plato in Timaeo probavit esse terram et ignem, per hoc quod necesse est corpora esse visibilia propter ignem, et palpabilia propter terram. 337. The second argument is at, also, the positive is prior to its privation [254]. With respect to it, it should be considered that contraries are always related according to "worse" and "better," as is said in Physics I, in such a way, namely, that one of them is a privation and a defect in comparison to the other, as are, for example, cold in relation to hot, and black in relation to white. Now, it is evident that affirmation, i.e., whatever is said positively as something complete, is prior to what is described in terms of privation and defect, as hot is prior to cold. But rest and heaviness, which are attributed to earth, are stated in terms of the privation of lightness and of motion, which are attributed to fire. Therefore, fire is naturally prior to earth. For if the subsequent is posited, so must be the prior. Consequently, if earth exists, fire too must exist. One should also note that Plato in the Timaeus proved that earth and fire exist on the ground that bodies have to be visible by virtue of fire and palpable by virtue of earth. 338. Deinde cum dicit: sed adhuc si quidem etc., ponit quartam conditionalem, scilicet quod si est ignis et terra, quod sint media elementa. Quia unumquodque elementorum habet aliqualiter contrarietatem ad unumquodque aliorum trium; sicut terra contrariatur igni secundum contrarietatem gravis et levis, et calidi et frigidi, aeri autem secundum contrarietatem calidi et frigidi, humidi et sicci: et hoc quidem dicit esse inferius manifestandum, praecipue in II De generatione. Unde relinquitur, si sunt duo elementa, quod necesse est esse alia duo, ex hoc quod probatum est quod si necesse est esse unum contrariorum, necesse est esse alterum. 338. Then, at but further, if [255], he proves the fourth conditional, namely, that if fire and earth exist, so do the intermediate elements. For each of the elements is in some respect contrary to each of the other three, as earth is contrary to fire on the basis of heavy and light and cold and hot, and is contrary to air according to a contrariety of hot and cold as well as of wet and dry. And he says that this is to be made clear below, especially in On Generation II. Hence, it remains that if two of the elements exist, the other two must also exist, it having been proved that if one contrary exists, the other must. Plato autem probavit ex extremis elementis quod necesse est esse media, per proportiones numerales: quia inter duos cubicos numeros necesse est esse duos alios numeros secundum continuam proportionalitatem; sicut cubicus binarii est octonarius, cubicus autem ternarii sunt viginti septem, inter quos cadunt media in proportione duodeviginti et duodecim, quae omnia se habent secundum sesquialteram proportionem. Plato, however, used proportional numbers to prove that if there are extreme elements there must be intermediate elements. For between two numbers that are cubes there must be two other numbers according to a continuous proportion: for example, the cube of 2 is 8 and the cube of 3 is 27 and between these cubes the numbers 18 and 12 fall as proportional means, so that all can be arranged to form a ratio of 3 to 2.