Quoniam autem corporum haec quidem sunt simplicia, haec autem composita ex his (dico autem simplicia quaecumque motus principium habent secundum naturam, puta ignem et terram et horum species et cognata his), necesse est et motus esse hos quidem simplices, hos autem mixtos aliqualiter: simplicium quidem simplices, mixtos autem compositorum, moveri autem secundum praedominans. 21 Bodies are either simple or compounded of such; and by simple bodies I mean those which possess a principle of movement in their own nature, such as fire and earth with their kinds, and whatever is akin to them. Necessarily, then, movements also will be either simple or in some sort compoundᾰsimple in the case of the simple bodies, compound in that of the compositeᾰand in the latter case the motion will be that of the simple body which prevails in the composition. 19. Postquam Philosophus ostendit universum esse perfectum et ratione suae corporeitatis et ratione suae universitatis, hic ostendit ex quibus partibus eius perfectio integratur. 19. After showing that the universe is perfect by reason both of its corporeity and its universalness, the Philosopher here shows from which parts its perfection is made up. Et primo dicit de quo est intentio; First, he expresses his intention; secundo ostendit propositum, ibi: omnia enim physica corpora et cetera. Secondly, he proves his proposition, at this seems to be. Circa primum considerandum est quod, sicut dicitur in III Physic., antiqui dixerunt infinitum esse extra quod nihil est. Quia igitur probavit universum esse perfectum ex hoc quod nihil est extra ipsum, sed omnia complectitur, posset aliquis suspicari ipsum esse infinitum. Et ideo huic opinioni occurrens, concludit subdens quod posterius intendendum est quantum ad naturam totius universi, si est infinitum secundum magnitudinem, sive finitum secundum totam suam molem. Interim tamen, antequam hoc tractetur, dicendum est de partibus eius quae sunt secundum speciem, in quibus scilicet integritas speciei ipsius consistit, cuiusmodi sunt simplicia corpora. Nam animalia et plantae et alia huiusmodi sunt secundariae partes eius, quae magis pertinent ad bene esse ipsius quam ad primam eius integritatem. Et hanc considerationem inchoabimus a principio infra posito. With respect to the first [13] it should be considered that, as is said in Physics III, the ancients described the infinite as that outside of which there is nothing. Now, since he has proved that the universe is perfect on the ground that nothing is outside it, but that it embraces all things, one might think it to be infinite. Accordingly, meeting this opinion, he concludes by adding that later on, in discussing the nature of the whole universe, there will be treated the question of whether it is infinite in magnitude, or finite with respect to its total mass. But meanwhile, before treating of this, something must be said about those parts of it that are according to the species, namely, those parts in which the integrity of its species consists, and which are the simple bodies. For animals and plants and other such are its secondary parts, and pertain more to the well-being of the universe than to its basic integrity. And we shall begin this consideration from a principle given below. 20. Deinde cum dicit: omnia enim physica etc., ostendit propositum, scilicet ex quibus partibus principalibus perfecta species universi integretur. 20. Then at all natural bodies he starts to manifest the proposition stating of which principal parts the perfect species of the universe is made. Et primo ostendit quod praeter quatuor elementa, necesse est esse aliud corpus simplex; secundo ostendit quod praeter quinque corpora simplicia non est aliud corpus, ibi: manifestum autem ex dictis et cetera. First, he shows that in addition to the four elements, another simple body must exist; secondly, that there is no simple body other than these five, at it is also clear from what has been said (L. 8). Circa primum duo facit: About the first he does two things: primo ostendit esse quintum corpus praeter quatuor elementa; first, he shows that there is a fifth body besides the four elements; secundo ostendit differentiam eius ad quatuor elementa, ibi: quoniam autem haec quidem supponuntur et cetera. secondly, how it differs from the four elements, at in consequence of what has been said (L. 5). Circa primum duo facit: With respect to the first he does two things: primo praemittit quaedam quae sunt necessaria ad propositum ostendendum; first, he mentions some preliminary facts needed in proving his proposition; secundo argumentatur ad propositum, ibi: si quidem igitur est simplex motus et cetera. secondly, he argues to the proposition supposing, then, that there is such a thing as simple movement (L. 4). Circa primum duo facit: About the first he does two things: primo praemittit quaedam quae pertinent ad motus; first, he premises facts regarding motion; secundo ponit quaedam quae pertinent ad corpora mobilia, ibi: quoniam autem corporum haec quidem et cetera. secondly, facts pertaining to mobile bodies, at bodies are either. Circa primum duo facit: About the first he does two things: primo praemittit continuitatem motus localis ad corpora naturalia; first, he mentions the connection between local motion and mobile bodies; secundo ponit distinctionem motuum localium, ibi: omnis autem et cetera. secondly, he distinguishes the kinds of local motion, at but all movement. 21. Dicit ergo primo quod omnia corpora physica, idest naturalia, dicimus esse mobilia secundum locum secundum seipsa, idest secundum sui naturam; et similiter alias magnitudines naturales, puta superficies et lineas, prout sunt termini naturalium corporum; ita tamen quod corpora per se moventur, aliae tamen magnitudines per accidens, motis corporibus. Et ad huius probationem inducit definitionem naturae, quae est principium motus in eis in quibus est, ut dicitur in II Physic. 21. He says therefore first [14] that all physical, i.e., natural, bodies are said to be mobile with respect to place according to themselves, i.e., according to their very natures, and the same is true for other natural magnitudes, e.g., planes and lines, insofar as they are the boundaries of natural bodies. And this is true in the sense that bodies are moved per se, but the other magnitudes per accidens, when the bodies are moved. In proof of this he adduces the definition of nature, which is the principle of motion in those things in which it exists, as is said in Physics II. Ex hoc autem sic argumentatur. Corpora naturalia sunt quae habent naturam: sed natura est principium motus in eis in quibus est: ergo corpora naturalia habent principium motus in seipsis. Sed quaecumque moventur quocumque motu, moventur localiter, non autem e converso, ut patet in VIII Physic., eo quod motus localis est primus motuum. Omnia ergo corpora naturalia moventur naturaliter motu locali, non autem omnia aliquo aliorum motuum. From this he argues thus: natural bodies are ones that have a nature, but nature is a principle of motion in things in which it is; therefore, natural bodies have a principle of motion in them. But whatever is moved with any sort of motion is moved locally, but not conversely, as is plain in Physics VII, because local motion is the first of motions. Therefore, all natural bodies are naturally moved with a local motion, but not all of them with all of the other motions. Sed videtur hoc esse falsum: caelum enim est corpus naturale, nec tamen eius motus videtur esse a natura, sed magis ab aliquo intellectu, sicut ex his quae determinantur in VIII Physic. et XII Metaphysic. patet. Sed dicendum est quod duplex est principium motus: unum quidem activum, quod est ipse motor, et tale principium motus animalium est anima: aliud autem est principium motus passivum, scilicet secundum quod corpus habet aptitudinem ut sic moveatur, et huiusmodi principium motus est in gravibus et levibus. Non enim componuntur ex movente et moto, ut philosophus dicit in VIII Physic.: quod quidem, inquit, nihil horum, scilicet gravium et levium, ipsum movet seipsum, manifestum est: sed motus habent principium, non movendi neque faciendi, sed patiendi. Sic igitur dicendum est quod principium activum motus caelestium corporum est intellectualis substantia: principium autem passivum est natura illius corporis, secundum quam natum est tali motu moveri. Et esset simile in nobis si anima non moveret corpus nostrum nisi secundum naturalem inclinationem eius, scilicet deorsum. This, however, seems to be false: for the heavens are a natural body, but their motion seems to be due, not to nature but to intellect, as is plain from what has been determined in Physics VIII and Metaphysics XII. But it must be said that there are two kinds of principles of motion: one is active, i.e., the mover, as the soul is the active principle of the motion of animals; the other is a passive principle of motion, i.e., a principle according to which a body has an aptitude to be thus moved, and such a principle of motion exists in the heavy and the light. For these are not composed of a mover and a moved, because, as the Philosopher says in Physics VIII, it is plain that none of these—i.e., the heavy and the light—moves itself, but each has, with respect to its motion, a principle not of causing motion or of acting, but of being acted upon. Consequently, it must be said that the active principle of the motion of heavenly bodies is an intellectual stance, but the passive principle is that body's nature according to which it is apt to be moved with such a motion. And the same situation would prevail in us, if the soul did not move our body in any way other than according to its natural inclination, namely, down. 23. Deinde cum dicit: omnis autem motus etc., ponit distinctionem localium motuum. 23. Then at but all movement he distinguishes local motions. Et primo distinguit communiter motus locales tam compositos quam simplices; First, he distinguishes in a general way both composite and simple local motions; secundo distinguit motus simplices, ibi: circulatio quidem igitur et cetera. secondly, he distinguishes simple motions, at now revolution about the center (268b20 ; [27]). Circa primum duo facit. With respect to the first he does two things: Primo proponit quod intendit, scilicet quod omnis motus localis (qui vocatur latio) aut est circularis, aut rectus, aut mixtus ex his, sicut motus obliquus eorum quae hac illacque feruntur. first (15), he proposes what he intends, namely, that every local motion—which is called latio—is either circular, or straight, or composed of these, as is the oblique motion of things that are borne this way and that. Secundo ibi: simplices enim etc., probat quod dixerat, per hoc quod motus simplices non sunt nisi duo, scilicet rectus et circularis. Et huius causam assignat ex hoc quod solae sunt duae magnitudines simplices, scilicet recta et circularis: motus autem localis secundum loca specificatur, sicut et quilibet alius motus secundum suos terminos. Secondly, at which are the only simple movements (16), he proves what he had said, on the ground that there are just two simple motions, the straight and the circular. And the reason for this, he says, is that there exist just two simple magnitudes, namely, the straight and the circular: but local motion is specified according to places, just as every other motion is specified according to its termini. 24. Sed videtur quod probatio Aristotelis non sit conveniens: quia, ut dicitur in I Poster., transcendentem in aliud genus non contingit demonstrare. Inconvenienter igitur per divisionem magnitudinum, quae pertinet ad mathematicum, concluditur aliquid circa motus, qui pertinent ad naturalem. Sed dicendum quod scientia quae se habet ex additione ad aliam, utitur principiis eius in demonstrando, sicut geometria utitur principiis arithmeticae: magnitudo enim addit positionem supra numerum, unde punctus dicitur esse unitas posita. Similiter autem corpus naturale addit materiam sensibilem supra magnitudinem mathematicam: et ideo non est inconveniens si naturalis in suis demonstrationibus utatur principiis mathematicis: non enim est omnino aliud genus, sed quodammodo sub illo continetur. 24. But it seems that Aristotle's proof is not suitable, because, as is said in Post. Anal. I, one does not demonstrate who crosses into another genus. Consequently, it seems unfitting to use the division of magnitudes, which pertain to mathematics, in order to reach a conclusion about motion, which pertains to natural science. But it must be said that a science which is by addition to some other science uses the latter's principles in demonstrating, as geometry uses the principles of arithmetic—for magnitude adds position to number, and thus a point is said to be a positioned unit. In like manner, natural body adds sensible matter to mathematical magnitude. Consequently, it is not unfitting for the natural philosopher in his demonstrations to use the principles of mathematics—for the latter is not of a completely different genus but is in a certain way contained under the former. Item videtur esse falsum quod solae duae magnitudines sint simplices, scilicet recta et circularis. Elix enim videtur esse una linea simplex, quia omnis pars eius est uniformis; et tamen linea elica nec est recta nec est circularis. Sed dicendum quod elix, si quis eius originem consideret, non est linea simplex, sed mixta ex recta et circulari. Causatur enim elix ex duobus motibus imaginatis, quorum unus est lineae circumeuntis columnam, alius autem est puncti moti per lineam: si enim uterque motus simul et regulariter perficiatur, constituetur elica linea per motum puncti in linea mota. Likewise, it seems to be false that only two magnitudes are simple, namely, the straight and the circular. For a helix [spiral] seems to be one simple line, because every one of its parts is uniform, and yet a helical line [such as a screw thread] is neither straight nor circular. But it must be said that a helix, if one considers its origin, is not a simple line, but a combination of straight and circular. For a helix is produced by two imaginary motions, one of which is the motion of a line moving round a cylinder, and the other of a point moving through the line: if two such motions take place in a regular manner at the same time, a helix will be formed by the motion of the point in the moving line. Item videtur quod motus circularis non sit simplex. Partes enim sphaerae circulariter motae non uniformiter moventur, sed pars quae est circa polos vel circa centrum, movetur tardius, quia peragit minorem circulum in eodem tempore: et ita motus sphaerae videtur compositus ex tardo et veloci. Sed dicendum quod continuum non habet partes in actu, sed solum in potentia: quod autem non est actu, non movetur actu: unde partes sphaerae, cum sint corpus continuum, non moventur actu. Unde non sequitur quod in motu sphaerico vel circulari sit diversitas actualis, sed solum potentialis; quae non repugnat simplicitati de qua nunc loquimur; omnis enim magnitudo habet pluralitatem potentialem. Likewise, it seems that circular motion is not simple. For the parts of a sphere that is in circular motion are not in uniform motion but the parts near the poles or near the center are moved more slowly, because they traverse a smaller circle in a given time; consequently, the motion of a sphere seems to be composed of fast and slow motions. But it must be said that a continuum does not have parts in act but only in potency. Now, what is not in act is not in actual motion. Hence the parts of a sphere, since they are a continuous body, are not actually being moved. Hence, it does not follow that, in a spherical or circular motion, there is actual diversity, but this is only potentially. This does not conflict with the simplicity about which we are now speaking, for every magnitude possesses potential plurality. 27. Deinde cum dicit: circulatio quidem igitur etc., distinguit motus simplices. 27. Then, at now revolution about the center (268b20), he distinguishes simple motions. Et primo ponit unum, scilicet circularem; First, he mentions one, namely, the circular; secundo ponit duos rectos, ibi: rectus autem etc.; secondly, he mentions two that are straight, at while the upward and downward movements (29); tertio concludit numerum ternarium simplicium motuum, ibi: itaque necesse et cetera. thirdly, he concludes that the number of simple motions is three, at all simple motion (30). Dicit ergo primo quod circulatio, idest motus circularis, dicitur qui est circa medium. Et est intelligendum circa mundi medium: rota enim, quae movetur circa medium sui, non movetur proprie circulariter; sed motus eius est compositus ex elevatione et depressione. He says therefore first [17] that circulation, i.e., circular motion is around the middle. And this is to be understood as around the middle of the world: for a wheel which is in motion around its own middle is not in circular motion in the proper sense of the word, but its motion is composed of ups and downs.