Accidit autem hoc et per sensum sufficienter, ut ad humanam dicere fidem. In omni enim praeterito tempore, secundum traditam invicem memoriam, nihil videtur transmutatum neque secundum totum extremum caelum, neque secundum partem ipsius propriam ullam. 38 The mere evidence of the senses is enough to convince us of this, at least with human certainty. For in the whole range of time past, so far as our inherited records reach, no change appears to have taken place either in the whole scheme of the outermost heaven or in any of its proper parts. Videtur autem et nomen ab antiquis datum esse usque ad tempus praesens, hoc modo existimantibus quo quidem et nos dicimus. Non enim semel neque bis, sed infinities oportet putare easdem advenisse opiniones ad nos, Propter quod, tanquam altero quodam existente primo corpore praeter terram et ignem et aerem et aquam, aethera appellaverunt supremum locum, a currere semper sempiterno tempore ponentes denominationem ipsi. Anaxagoras autem utitur nomine hoc non bene: nominat enim aethera pro igne. 39 The common name, too, which has been handed down from our distant ancestors even to our own day, seems to show that they conceived of it in the fashion which we have been expressing. The same ideas, one must believe, recur in men's minds not once or twice but again and again. And so, implying that the primary body is something else beyond earth, fire, air, and water, they gave the highest place a name of its own, aither, derived from the fact that it 'runs always' for an eternity of time. Anaxagoras, however, scandalously misuses this name, taking aither as equivalent to fire. Postquam Philosophus ostendit quod corpus quintum non est subiectum generationi et corruptioni, hic ostendit quod non est subiectum augmento et deminutioni. Et utitur tali ratione. Omne corpus augmentabile est quantum ad aliquid subiectum generationi et corruptioni. Ad cuius manifestationem proponit quod omne corpus augmentabile augetur per appositionem alicuius connaturalis advenientis; quod quidem, cum prius esset dissimile, factum est simile per resolutionem in propriam materiam, quae, deposita forma priori, formam corporis augmentandi assumpsit; sicut panis, resolutus in materiam, accipit formam carnis, et ita per additionem ad carnem praeexistentem facit augmentum. Unde ubicumque est augmentum, ibi oportet quod sit generatio et corruptio in aliquid. Corpori autem caelesti non est dare aliquid ex quo sit generatum, ut ostensum est. Ergo non potest esse augmentabile vel deminuibile. After showing that the fifth body is not subject to generation and corruption, the Philosopher here shows that it is not subject to increase and diminution [35] and uses this argument: every augmentable body is, with respect to something, subject to generation and corruption. To explain this, he proposes that every augmentable body is increased by the addition of something connatural that comes to it. This, indeed, while being first unlike, has become like by being resolved into its proper matter which, doffing its previous form, has assumed the form of the body to be increased—as bread, after being resolved into matter, receives the form of flesh, and thus, through being added to pre-existing flesh, produces increase. Hence wherever there is growth there must be generation and corruption into something. But there is nothing from which a heavenly body can be generated, as has been shown. Therefore it cannot be augmentable or decreasable. 72. Deinde cum dicit: si autem est etc., ostendit quod non sit subiectum alterationi. Posset autem videri alicui quod brevis via removendi alterationem a corpore caelesti, esset per remotionem contrarietatis: sicut enim generatio est ex contrariis, ita et alteratio. Sed advertendum quod Aristoteles removit contrarietatem a quinto corpore removendo ab eo contrarietatem motus: alteratio autem videtur fieri non solum secundum contrarietatem cui respondent contrarii motus locales, quae est gravis et levis et eorum quae assequuntur; sed etiam secundum alia contraria quae ad hoc non pertinent, puta secundum album et nigrum: et ideo utitur alia via, quae sumitur ex parte augmenti. Et dicit quod eiusdem rationis est aestimare quod corpus caeleste non sit alterabile, et quod non sit augmentabile seu corruptibile. Quia alteratio est motus secundum qualitatem, ut dictum est in V Physic. Alteratio autem, ut in VII Physic. ostensum est, proprie fit secundum tertiam speciem qualitatis, quae est passio et passibilis qualitas: quamvis enim habitus et dispositio pertineant ad genus qualitatis, non tamen causantur sine transmutatione quae fit secundum passiones; sicut sanitas et languor proveniunt ex transmutatione frigidi et calidi, humidi et sicci. Omnia autem corpora naturalia quae transmutantur secundum passionem vel passibilem qualitatem, per consequens videntur habere augmentum et decrementum; sicut patet de corporibus animalium et de partibus eorum, et etiam de plantis, in quibus proprie est augmentum. Ita etiam est de elementis: quae quidem secundum transmutationem calidi et frigidi rarefiunt et condensantur, et per consequens transmutantur in maiorem vel minorem quantitatem, quod est quodammodo augeri et deminui. Sic igitur patet quod, si corpus quod circulariter movetur, non subiacet augmento vel decremento, quod etiam non subiaceat alterationi. 72. Then, at and if it is exempt from increase [36] he shows that it is not subject to alteration. Now it might seem to someone that an easy way to remove alteration from the heavenly body would be by removing contrariety, for just as generation occurs from contraries, so too, does alteration. But it should be observed that Aristotle removed contrariety from the fifth body by removing from it contrariety of motion. Alteration, however, seems to occur not only according to the contrariety to which contrary local motions correspond, namely, heavy and light and whatever results from them, but also according to other contraries which do not pertain to this, for example, according to black and white. Accordingly, he uses another way, based on increase. And he says that it is for the same reason that we estimate a heavenly body not to be alterable and not to be augmentable or perishable. For alteration is a motion affecting quality, as has been said in Physics V. But alteration, as was shown in Physics VII, properly takes place according to the third species of quality, which is "passion and passible quality": for although "habit and disposition" pertain to [the first species of] the genus of quality, they are not produced without a change made according to the passions, just as health and languor result from a change of cold and hot, moist and dry. Now all natural bodies that are changed with respect to passion or passible quality seem as a consequence to have growth and decrease, as is clear from the bodies of animals and their parts and even of plants, in which growth properly exists. The same applies also to the elements, which rarefy and condense with respect to a change in hot and cold, from which results a change into larger or smaller quantity which is in a sense the same as being increased and decreased. Thus it is plain that if a body which is moved circularly is not subject to increase or decrease it is not subject to alteration. Ultimo autem epilogando concludit manifestum esse ex dictis, si quis velit assentire prioribus demonstrationibus, non proterve contradicendo, quod corpus primum, quod scilicet movetur motu primo et perfecto, idest circulari, est sempiternum, quasi non subiacens generationi et corruptioni; neque etiam habet augmentum neque decrementum; et non subiacet senectuti, neque alterationi, neque passioni. Finally, in summary he concludes that it is plain from the foregoing—if anyone wants to assent to the previous demonstrations without wantonly contradicting — that the first body, which, namely, is moved with the first and perfect motion, i.e., circular motion, is sempiternal (as not being subject to generation and corruption), that it undergoes neither increase nor decrease, and that it is not subject to aging or alteration or passion. 73. Potest autem obiici contra hanc Aristotelis rationem dupliciter. 73. Nevertheless, objections can be leveled against this argument of Aristotle on two counts. Primo quidem contra conclusionem. Videtur enim esse falsum quod corpus caeleste non alteretur: manifeste enim apparet lunam a sole illuminari, et per umbram terrae obscurari. Dicendum est autem quod duplex est alteratio. Una quidem passiva, secundum quam ita aliquid adiicitur, quod etiam aliquid aliud abiicitur; sicut cum aliquid alteratur de calido in frigidum, amittit calorem et recipit frigiditatem: et talem alterationem, quae fit secundum passiones, intendit hic philosophus excludere a corpore caelesti. Est autem alia alteratio perfectiva, quae fit secundum quod aliquid ab alio perficitur absque alterius abiectione, qualem alterationem ponit Philosophus in II De anima etiam in potentia sensitiva: et talem alterationem nihil prohibet esse in corporibus caelestibus, quorum quaedam recipiunt virtutes ab aliis secundum coniunctiones et varios aspectus, absque hoc quod aliquod eorum propriam virtutem amittat. First of all against the conclusion. For it seems to be false that a heavenly body is not altered, for it is plainly evident that the moon is illumined by the sun and obscured by the shadow of the earth. But it must be said that alteration is of two kinds. One is passive and according to it things are so added that something else is cast off, as, when something is altered from hot to cold, it loses heat and receives coldness. It is that kind of alteration, which takes place according to passions, that the Philosopher is here excluding from heavenly body. But there is another kind of alteration which is perfecting, which occurs insofar as something is perfected by something else without loss to the former—this is the kind of alteration that the Philosopher in On the Soul II posits even in a sense power. Such an alteration nothing prevents from being in heavenly bodies, some of which receive virtues from others according to conjunctions and various aspects, but without any of them losing their own virtue. 74. Secundo obiicitur contra processum rationis hic inductae: non enim videtur esse verum quod quaecumque alterantur, augmentum et decrementum suscipiant. Augmentum enim et decrementum fit per additionem alicuius quod est conversum in substantiam eius quod augetur, ut dicitur in libro De generat. et in II De anima; et etiam hoc supra dictum est. Hic autem motus augmenti non est nisi in animalibus et plantis: nam ea quae rarefiunt et condensantur, non augentur ex aliquo addito, ut probatur in IV Physic. Inconvenienter igitur videtur hic Aristoteles attribuere motum augmenti non solum animalibus et plantis et partibus eorum, sed etiam elementis. Dicendum est autem quod Aristoteles hic loquitur de augmento pro quolibet motu quo aliquid proficit in maiorem quantitatem. Nondum enim perfecte explicaverat naturam motus augmenti: est autem suae consuetudinis ut ante manifestationem veritatis, utatur opinionibus communibus. Nec impedit virtutem probationis eius, quod supra exclusit augmentum a corpore caelesti per exclusionem additionis corporis in ipsum quod augetur transmutati: quia sicut quod augetur per additionem, non est omnino liberum a generatione et corruptione, ita etiam quod augetur per rarefactionem. 74. The second objection is directed against the procedure of his argument: for it does not seem to be true that whatever is altered receives increase and decrease. For these result from the addition of something that is converted into the substance of what is increased, as is said in the book On Generation and in On the Soul II, and as was said above. Now the motion of increase does not exist except in animals and plants, for things that rarefy and condense are not increased by the addition of anything, as was proved in Physics V. Consequently, it seems unsuitable for Aristotle here to attribute the motion of increase not only to animals and plants and their parts, but to the elements as well. But it should be said that Aristotle is here speaking of increase in the sense of any motion by which something proceeds to greater quantity. For he has not yet perfectly explained the nature of the motion of increase and it is his custom, before he has shown the true view, to use common opinions. But the force of his proof is not impeded by his having excluded increase from a heavenly body by excluding addition of a body changed into what is increased: for just as anything increased by addition is not utterly free of generation and corruption, so, too, what is increased by rarefaction. Est autem considerandum quod signanter in hac ratione mentionem facit de corporibus physicis: quia in corporibus mathematicis potest esse augmentum sine alteratione, puta cum quadratum crevit apposito gnomone, sed non est alteratum, ut dicitur in praedicamentis; et e converso potest aliquid alterari sine hoc quod augeatur, sicut cum fit triangulus aequalis quadrato. However, it is to be noted that in this proof he makes mention of physical bodies advisedly, because in mathematical bodies increase can occur without alteration—for example, a square grows by adding to it a gnomon, but it is not altered, as is said in the Predicaments; conversely, a thing can be altered without being increased, as when a triangle is made equal to a square. 75. Deinde cum dicit: videtur autem etc., manifestat propositum per signa. Et dicit quod ratio et ea quae apparent probabiliter videntur in materia ista sibi invicem testificari. Et ponit tria signa. 75. Then, at the common name, too [37], he manifests the proposition through signs. And he says that both reason and things that appear to be probable seem to support one another on this point. And he gives three signs. Quorum primum est ex communi hominum opinione, qui ponunt multos deos, vel unum Deum, cui alias substantias separatas deservire dicunt; et omnes sic opinantes attribuunt supremum locum, scilicet caelestem, Deo, sive sint barbari sive Graeci, quicumque scilicet putant esse res divinas. Sic autem attribuunt caelum divinis substantiis, quasi adaptantes immortalem locum immortalibus et divinis rebus; ut sic habitatio Dei in caelo intelligatur esse secundum similitudinis adaptationem, quia scilicet hoc corpus inter cetera corpora magis accedit ad similitudinem spiritualium substantiarum et divinarum. Est enim impossibile quod aliter Deo habitatio caeli attribuatur, quasi indigeat loco corporali a quo comprehendatur. Si igitur ponendae sint res divinae, immo quia pro certo ponendae sunt, consequens est quod bene sint dicta ea quae dicta sunt de prima substantia corporali, scilicet de corpore caelesti, quod scilicet est ingenitum et impassibile. Quamvis autem existimant homines templa esse locum Dei, hoc tamen non existimant ex parte ipsius Dei, sed ex parte colentium Deum, quos oportet in aliquo loco Deum colere. Unde templa corruptibilia sunt proportionalia hominibus corruptibilibus, caelum autem incorruptioni divinae. The first of which is taken from the general opinion of men, who posit many gods or one God, whom the other separated substances serve. All who believe thus, whether Greeks or barbarians, assign the highest place, namely, the heavenly, to God, namely, all those who believe there are divine beings. But they assign the heavens to the divine substances as though adapting an immortal place to immortal and divine beings. In this way God's habitation in the heavens is understood as appropriate according to likeness, that is, that among all other bodies this body more closely approaches to a likeness to spiritual and divine substances. For it is impossible for the habitation of the heavens to be assigned to God for any other reason, as though he should need a bodily place by which he is comprehended. If therefore divine beings are to be posited, and since, indeed, they certainly must, the consequence is that the statements made about the first bodily substance, namely, the heavenly body, were well made, namely, that the heavenly body is ungenerated and unalterable. Although men suppose that temples are the place of God, they do not suppose this from God's viewpoint but from that of the worshippers, who must worship him in some place. That is why perishable temples are proportioned to perishable men, but the heavens to the divine imperishability. 76. Secundum signum ponit ibi: accidit autem hoc et per sensum etc.: quod quidem accipitur ab experientia longi temporis. Et dicit quod id quod probatum est per rationem et per communem opinionem, accidit, idest consequitur, sufficienter; non quidem simpliciter, sed sicut potest dici per comparationem ad humanam fidem, idest quantum homines possunt testificari de his quae parvo tempore et a remotis viderunt. Secundum enim memoriam quam sibi invicem tradiderunt astrologi, dispositiones et motus caelestium corporum observantes, in toto praeterito tempore non videtur aliquid transmutatum esse neque secundum totum caelum, neque secundum aliquam propriam partem eius. Quod quidem non esset si caelum generabile et corruptibile esset: quaecumque enim generantur et corrumpuntur, paulatim et successive ad perfectum statum perveniunt, et ex eo paulatim recedunt: quod quidem non posset tanto tempore latere in caelo, si naturaliter generationi et corruptioni subiaceret. Nec tamen hoc est necessarium, sed probabile. Quanto enim aliquid est diuturnius, tanto maius tempus requiritur ad hoc quod eius mutatio deprehendatur; sicut transmutatio hominis non deprehenditur in duobus vel tribus annis, in quibus deprehenditur transmutatio canis, vel alicuius alterius animalis breviorem vitam habentis. Posset igitur aliquis dicere quod, etsi caelum sit naturaliter corruptibile, est tamen tam diuturnum, quod totum tempus cuius memoria potest haberi, non sufficit ad deprehendendam eius transmutationem. 76. The second sign he gives at the mere evidence of the senses [38] and it is taken from long experience. And he says that what has been proved by reason and common opinion occurs, i.e., follows, sufficiently—i.e., not absolutely but to the extent of human faith, i.e., so far as men can testify to what they have seen for a short time and from afar. For according to the tradition which astronomers have passed on concerning their observations of the dispositions and motions of heavenly bodies, in the whole time past there does not seem to have been any change affecting either the entire heavens or any of its own parts. Now this would not be, if the heaven were generable or perishable—for things subject to generation and corruption arrive at their perfect state little by little and step by step, and then gradually depart from that state, and this could not have been concealed in the heavens for such a long time, if they were naturally subject to generation and corruption. However, this is not necessary but probable. For the more lasting something. is, the greater the time required for its change to be noted, just as change in a man is not noticed in two or three years, as it is in a dog or other animals having a shorter life-span. Consequently, someone could say that, even though the heavens are naturally corruptible, nevertheless, they are so lasting that the whole extent of human memory is not sufficient to observe their change. 77. Tertium signum ponit ibi: videtur autem et cetera. Quod quidem sumitur a nomine imposito ab antiquis, quod durat usque ad praesens tempus; per quod datur intelligi quod ipsi etiam hoc modo opinabantur caelum esse incorruptibile, sicut nos opinamur. Et ne aliquis contra hoc obiiceret quod aliqui ante suum tempus, caelum generabile et corruptibile posuerunt, subiungit quod opiniones verae renovatae sunt secundum diversa tempora non semel aut bis, sed infinities, supposita infinitate temporis. Destruuntur enim studia veritatis per diversas mutationes in his inferioribus accidentes: sed quia mentes hominum naturaliter inclinantur ad veritatem, cessantibus impedimentis, renovantur studia, et homines tandem perveniunt ad opiniones veras quae prius fuerant: opiniones autem falsas non necesse est renovari. Et ideo antiqui, opinantes quod primum corpus, scilicet caeli, esset alterius naturae praeter quatuor elementa, nominaverunt supremum locum mundi aethera, ponentes scilicet ei nomen ab eo quod semper currit sempiterno tempore: thein enim in Graeco idem est quod currere. Sed Anaxagoras male interpretatus est hoc nomen, attribuens ipsum igni, quasi caeleste corpus sit igneum: aethein enim in Graeco idem est quod ardere, quod est proprium ignis. Sed quod caeleste corpus non sit igneum, patet ex supra dictis. 77. The third sign is given at the common name, too [39], and is based on a name given by the ancients, which endures to the present, and which gives us to understand that they thought the heaven to be imperishable just as we do. And lest anyone object that some before their time thought the heavens were subject to generation and corruption, he adds that true opinions are revived according to diverse times not once or twice but infinitely, supposing that time is infinite. For the studies of truth are destroyed by various changes occurring in these lower things, but because the minds of men are naturally inclined to truth, then when obstacles are removed, studies are renewed and men at last arrive at the true opinions which previously flourished, but false opinions need not be revived. Consequently the ancients, supposing that the first body, namely, the heaven, to be of a nature different from the four elements, named the highest place of the world the "aether," thus applying to it a name based on the fact that it always runs for an eternity of time—for thein in Greek is the same as "to run." But Anaxagoras misinterpreted this name, attributing it to fire, as though the heavenly body were fiery — for aether in in Greek is the same as "to burn," which is proper to fire. But that a heavenly body is not of fire is plain from what has been said above [in L. 4]. Lectio 8 Lecture 8 Ad integritatem universi non requiritur praeter quinque corpora simplicia aliquod corpus simplex probatur motui circulari non esse aliquem motum contrarium Only five simple bodies required. No motion contrary to circular. Manifestum autem ex dictis quia et numerum impossibile est esse maiorem dictorum corporum simplicium. Simplicis quidem enim corporis necesse motum simplicem esse: solos autem hos esse dicimus simplices, eum qui circum, et eum qui in rectum, et huius duas partes, hunc quidem a medio, hunc autem ad medium. Quod autem non est circulationi contraria alia latio, ex multis utique quis accipiet fidem. 41 It is also clear from what has been said why the number of what we call simple bodies cannot be greater than it is. The motion of a simple body must itself be simple, and we assert that there are only these two simple motions, the circular and the straight, the latter being subdivided into motion away from and motion towards the center. That there is no other form of motion opposed as contrary to the circular may be proved in various ways. Primum quidem quia circulari rectum opponi maxime ponimus. Concavum enim et gibbosum non solum ad invicem opponi videntur sed et recto, combinata et iuxta se posita. Itaque, si quidem contraria aliqua est latio, eam in recto maxime necessarium contrariam esse ad eum qui in circuitu motum. Quae autem in recto, ad invicem opponuntur propter loca: quod enim sursum ei quod deorsum et loci est differentia et contrarietas. 42 In the first place, there is an obvious tendency to oppose the straight line to the circular. For concave and convex are a not only regarded as opposed to one another, but they are also coupled together and treated as a unity in opposition to the straight. And so, if there is a contrary to circular motion, motion in a straight line must be recognized as having the best claim to that name. But the two forms of rectilinear motion are opposed to one another by reason of their places; for up and down is a difference and a contrary opposition in place. Deinde, si quis existimat eandem rationem esse quam et in recto, et in circulari (eam enim quae ab A ad B lationem, contrariam ei quae a B ad A), eam quae in recto dicit: hae enim finitae sunt. Circulares autem infinitae utique erunt circa eadem signa. 43 Secondly, it may be thought that the same reasoning which holds good of the rectilinear path applies also the circular, movement from A to B being opposed as contrary to movement from B to A. But what is meant is still rectilinear motion. For that is limited to a single path, while the circular paths which pass through the same two points are infinite in number. Similiter autem et quae in semicirculo uno, puta a G ad D et a D ad G. Eadem enim ei est quae in diametro est: semper enim unumquodque distare secundum rectum ponimus. 44 Even if we are confined to the single semicircle and the opposition is between movement from C to D and from D to C along that semicircle, the case is no better. For the motion is the same as that along the diameter, since we invariably regard the distance between two points as the length of the straight line which joins them. Similiter autem et utique si quis circulum faciens, eam quae in altero semicirculo lationem, contrariam ponat ei quae in altero; puta in toto circulo eam quae ab E ad Z eius qui I semicirculi, ei quae a Z ad E in T semicirculo. 45 It is no more satisfactory to construct a circle and treat motion 'along one semicircle as contrary to motion along the other. For example, taking a complete circle, motion from E to F on the semicircle G may be opposed to motion from F to E on the semicircle H. Si autem et istae contrariae, sed nunquam et quae in toto circulo invicem propter hoc contrariae. 46a But even supposing these are contraries, it in no way follows that the reverse motions on the complete circumference contraries. At vero neque quae ab A ad B circulatio, contraria ei quae ab A ad G. Ex eodem enim in idem motus: contraria autem determinata est latio ex contrario in contrarium esse. 46b Nor again can motion along the circle from A to B be regarded as the contrary of motion from A to C: for the motion goes from the same point towards the same point, and contrary motion was distinguished as motion from a contrary to its contrary. Si autem et esset quae circum, ei quae circum contraria, frustra utique esset altera. Ad eadem enim: quia necesse est quod circumfertur, undecumque incipiens, in omnia similiter advenire contraria loca. Sunt autem loci contrarietates sursum et deorsum, ante et retro, et dextrum et sinistrum: lationis autem contrarietates secundum locorum contrarietates sunt. Si quidem enim aequales essent, non utique esset motus ipsarum: si autem alter motus dominaretur, alter utique non esset. Itaque, si ambo essent, frustra utique esset alterum corpus non motum eodem motu: frustra enim calceamentum hoc dicimus cuius non est calceatio. Deus autem et natura nihil frustra faciunt. 47 And even if the motion round a circle is the contrary of the reverse motion, one of the two would be ineffective: for both move to the same point, because that which moves in a circle, at whatever point it begins, must necessarily pass through all the contrary places alike. (By contrarieties of place I mean up and down, back and front, and right and left; and the contrary oppositions of movements are determined by those of places.) One of the motions, then, would be ineffective, for if the two motions were of equal strength, there would be no movement either way, and if one of the two were preponderant, the other would be inoperative. So that if both bodies were there, one of them, inasmuch as it would not be moving with its own movement, would be useless, in the sense in which a shoe is useless when it is not worn. But God and nature create nothing that has not its use. 78. Postquam Philosophus ostendit necesse esse aliquod corpus praeter quatuor elementa, hic ostendit quod praeter ista corpora non requirit integritas universi aliquod aliud corpus. 78. After showing the necessity of some body besides the four elements, the Philosopher here shows that the integrity of the universe requires no other body besides these five. Et primo ostendit propositum; First he shows his proposition; secundo probat quoddam quod supposuerat, ibi: quod autem non est circulationi et cetera. secondly, he proves something he had assumed, at that there is no other form of motion 79. Dicit ergo primo quod ex dictis, quibus probatum est esse quintum corpus praeter corpora gravia et levia, potest etiam manifestari quod impossibile est esse maiorem numerum simplicium corporum. Quia, sicut supra dictum est, necesse est quod cuiuslibet simplicis corporis sit aliquis motus simplex. Sed non est alius motus simplex praeter praedictos, quorum unus est circularis et alius est rectus, qui in duas partes dividitur: nam motuum rectorum unus quidem est a medio, qui dicitur motus sursum; alius autem est ad medium, qui dicitur motus deorsum. Horum autem motuum ille qui est ad medium, est corporis gravis, scilicet terrae et aquae; ille autem qui est a medio, est corporis levis, scilicet ignis et aeris; ille autem qui est circularis, est primi et supremi corporis. Unde relinquitur quod praeter praedicta corpora simplicia non sit aliquod aliud corpus simplex: et ita integritas universi ex istis quinque corporibus consistit. He says therefore first [40] that from what was said in proving that there exists a fifth body in addition to heavy and light bodies, it can be shown that it is impossible for a greater number of simple bodies to exist. For as was said above, for each simple body there must be some simple motion. But there is no simple motion other than the ones previously mentioned: one of which is circular and the other straight, the latter being divided into two kinds, one of which is from the middle and is called "upward motion" and the other toward the middle and is called "downward motion." Of the latter two, the one which is toward the middle belongs to a heavy body, namely, to earth and water, while the one from the middle belongs to a light body, namely, to fire and air. Finally, the circular motion is assigned to the first and supreme body. Hence, what remains is that there is no other simple body besides the ones mentioned. Consequently, the wholeness of the universe consists of these five bodies. 79. Deinde cum dicit: quod autem non est circulationi etc., probat quoddam quod supposuerat, scilicet quod motui circulari non sit aliquis motus contrarius. Et hoc quidem supposuerat in demonstratione qua probavit corpus caeli non esse subiectum generationi et corruptioni: sed ideo non statim ibi probavit, sed distulit probationem usque huc, quia hoc etiam valet ad ostendendum quod non sit maior numerus simplicium corporum. Si enim motui circulari esset aliquis motus contrarius, posset dici quod sicut est duplex corpus quod movetur motu recto, propter contrarietatem huius motus, ita etiam est duplex corpus quod movetur motu circulari. Hoc autem non continget, si constet quod corpori circulari non sit aliquis motus contrarius. Circa hoc ergo primo proponit quod intendit. Et dicit quod per multas rationes potest aliquis accipere fidem quod motui circulari non sit aliquis motus localis contrarius. 79. Then, at that there is no other form of motion [41] he proves something he had assumed, namely, that there is not a motion contrary to circular motion. This he had assumed in the discussion in which he proved that the body of the heavens is not subject to generation and corruption. But the reason why he did not prove it right away, but waited until now, is that it is also useful in proving that there is not a greater number of simple bodies. For if there were a motion contrary to circular motion, it could be held that just as there are two bodies moved with straight motion on account of the contrariety of this motion, so there are also two bodies moved with circular motion. But this will not occur if it is plain that there is no motion contrary to circular motion. Therefore, on this point, first he proposes what he intends, and says that there are many reasons to induce one to believe that there is not a circular motion contrary to circular motion. 80. Secundo ibi: primum quidem etc., ostendit propositum. Circa quod considerandum est quod, si in motu circulari sit contrarietas, oportet hoc esse altero trium modorum: quorum unus est ut motui circulari rectus sit contrarius, alius modus est ut sit aliqua contrarietas in ipsis partibus motus circularis, tertius est ut uni motui circulari alius motus circularis contrarietur. 80. Secondly, at in the first place, he establishes the proposition. In regard to this it must be noted that if there exists contrariety in circular motion, it must be in one of three ways: one is that a straight motion be contrary to circular motion; the second is that there be some sort of contrariety in the parts themselves of circular motion; the third is that one circular motion have some other circular motion contrary to it. Primo ergo ostendit quod motui circulari non contrariatur motus rectus; First, therefore, he shows that a straight motion is not contrary to circular motion; secundo ostendit quod non sit contrarietas in partibus motus circularis, ibi: deinde si quis existimat etc.; secondly, he shows that there is no contrariety in the parts of circular motion, at secondly, it may be thought 10.83; tertio quod non sit contrarietas in toto motu circulari, unius scilicet motus circularis ad alium, ibi: at vero neque quae ab a et cetera. thirdly, that there is no contrariety between complete circular motions, i.e., of one to another, at nor again can motion along the circle from A 89. 81. Dicit ergo primo quod maxime circulari videtur opponi rectum. Linea enim recta nullam fractionem habet; figura autem angularis habet quandam fractionem, non per totum, sed in angulis; sed figura circularis videtur per totum habere fractionem, ac si totum esset angulus. Et secundum hoc rectum et circulare videntur esse contraria quasi maxime distantia. Et quia posset aliquis dicere quod circulari non opponitur rectum, sed concavo opponitur convexum sive gibbosum, ad hanc obviationem excludendam, subiungit quod concavum et gibbosum, idest convexum, non solum videntur habere oppositionem ad invicem, sed etiam ad rectum. Ad se invicem autem videntur habere oppositionem sicut combinata et iuxta se posita, idest secundum relationem: nam concavum dicitur respectu eorum quae intra sunt, gibbosum autem respectu eorum quae sunt extra. Et sic omni modo rectum contrariatur circulari, sive accipiatur sub ratione concavi, sive sub ratione convexi. Et quia contrarietas motuum videtur esse secundum contrarietatem eorum in quibus est motus, videtur esse consequens quod si aliquis motus sit contrarius motui circulari, maxime sit ei contrarius motus rectus, qui scilicet est super lineam rectam. Sed motus recti contrariantur ad invicem, propter loca contraria (motus enim qui est sursum, contrariatur ei qui deorsum est, quia sursum et deorsum important differentiam et contrarietatem loci): et sic uni motui recto contrariabitur alius motus rectus, et circularis. Hoc autem est impossibile: quia uni unum est contrarium. Ergo impossibile est quod motui circulari sit aliquis motus contrarius. 81. He says therefore first [42] that what seems most opposite to something circular is something straight. For a straight line has no break, while an angular line does have a break, not through the whole, but in the angles; meanwhile a circular figure seems to have breaks throughout, as if the whole were an angle. According to this the straight and the circular seem to be contraries, as though at the farthest extremes. And because someone could say that it is not the straight that is opposed to the circular, but rather the convex or gibbous which is opposed to the concave, to reject this objection, he adds that concave and gibbous, i.e., convex, are seen to be opposed not only to one another, but to the straight as well. They seem to be mutually opposed after the manner of the combined and the juxtaposed, i.e., in terms of relation: for "concave" is said in relation to things that are inside [a circle or sphere], but "gibbous" with respect to things outside. Consequently, from every aspect, the straight is contrary to the circular, whether taken as concave or as convex. And because the contrariety of motions is seen to follow the contrariety of the things in which the motion is, the consequence seems to be that if there is a motion contrary to circular motion, it should be most of all straight motion which, namely, is over a straight line. But straight motions are contrary to one another because of contrary places—for upward motion is contrary to downward because "up" and "down" imply a difference and contrariety of place. Consequently, one straight motion will have as its contrary some other straight motion, and a circular one. This, however, is impossible, for to one thing there is one contrary. Therefore, it is impossible for any motion to be contrary to circular. 82. Potest autem aliquis obiicere contra hoc quod dicitur, quod circulari maxime contrariatur rectum. Dictum est enim in Praedicamentis quod figurae nihil est contrarium: rectum autem et circulare sunt differentiae figurarum. Potest autem dici quod philosophus hic ex hypothesi loquitur, et non simpliciter. Si enim aliquid esset contrarium circulari, maxime contrariaretur sibi rectum, ratione supra dicta. Potest etiam dici quod in quolibet genere invenitur contrarietas differentiarum, ut patet X Metaphys., licet non sit in omni genere contrarietas specierum: etsi enim rationale et irrationale sint contrariae differentiae, non tamen homo et asinus sunt contrariae species. Sic igitur ponitur contrarietas inter rectum et circulare, non sicut inter species, sed sicut inter differentias eiusdem generis. Huiusmodi autem contrarietas, quae posset attendi in motibus secundum differentiam recti et circularis, non est contrarietas corruptiva, qualem intendit hic Philosophus excludere a corpore caelesti, sicut est contrarietas calidi et frigidi: contrarietatem autem secundum differentias aliquorum generum nihil prohibet in corpore caelesti esse, puta sicut par vel impar, vel secundum aliquid huiusmodi. 82. But someone could object to the statement that the straight is most contrary to the circular. For it is stated in the Predicaments that nothing is contrary to figure, whereas "straight" and "circular" are differences in figure. But it can be said that the Philosopher is here speaking hypothetically and not categorically. For if anything were contrary to the circular, it would be the straight most of all, for the reason given above. It can also be said that in every genus there is found a contrariety of differences, as is plain from Metaphysics X, although there is not a contrariety of species in every genus: for although "rational" and "irrational" are contrary differences, "man" and "ass" are not contrary species. Consequently, there is a contrariety between straight and circular not as between species, but as between differences of the same genus. Such contrariety, which can be discerned in motions on the basis of the difference between straight and circular, is not a corruptive contrariety, of the sort, namely, which the Philosopher here intends to exclude from the heavenly body, such as is the contrariety of hot to cold. But nothing forbids contrariety according to the differences of certain genera from being in a heavenly body, for example, that of equal and unequal, or something of that kind. Obiicit autem Ioannes grammaticus contra id quod philosophus videtur ponere concavum et gibbosum opponi secundum relationem: quia relativa videntur simul esse, concavum autem et gibbosum non sunt simul ex necessitate: potest enim esse aliquod corpus sphaericum exterius convexum absque hoc quod sit interius concavum. Sed in hoc deceptus fuit: quia Philosophus hic loquitur de concavo et convexo secundum quod inveniuntur in linea circulari, non autem secundum quod inveniuntur in corpore sphaerico, in quo unum potest esse sine altero, non autem in linea. John the Grammarian, however, objects against the Philosopher's seeming to state that concave and gibbous are opposed according to a relation: because relative things seem to be co-existent, but concave and gibbous are not necessarily together, for a spherical body can be exteriorly convex without being interiorly concave. But in this he has been deceived, for the Philosopher is here speaking of concave and convex as found in a circular line, and not as found in a spherical body, in which latter one can indeed exist without the other, but not in a line. 83. Deinde cum dicit: deinde si quis existimat etc., ostendit non esse contrarietatem in partibus motus circularis. 83. Then, at secondly, it may be thought [43] he shows that there is no contrariety in the parts of circular motion.