Authors/Thomas Aquinas/physics/L7/lect8

Lecture 8 Which motions may be compared

Latin	English
	Lecture 8 Which motions may be compared
lib. 7 l. 8 n. 1 Postquam philosophus ostendit in communi, quid requiratur ad hoc quod aliqua sint comparabilia, applicat inventam veritatem ad comparationem motuum, de qua hic intendit. Et primo in communi; secundo comparando motus diversorum generum, ibi: si autem aliud etc.; tertio comparando motus unius generis ad invicem, ibi: quare si quae in aequali et cetera. Dicit ergo primo, quod sicut in aliis requiritur ad hoc quod sint comparabilia, quod non sint aequivoca, et quod sit idem primum susceptivum, et quod sit eadem species; sic et circa motum aeque velox dicitur illud quod movetur in aequali tempore, per tantum et aequale alterius longitudinis, in hac, idest secundum mutationem eiusdem speciei.	940. After pointing out in general what is required in order that things be able to be compared, the Philosopher now applies the truth found to the comparison of motions. First in general; Secondly, by comparing motions that belong to diverse genera, at 941; Thirdly, by comparing one motion to another in the same genus, at 942. He says therefore first (722 249 a8) that just as in other matters the requirements for comparability are that the things compared be not equivocal, and that there be an identical first receiver, and that they be of the same species, so also in regard to motion, “equally swift” is said of things that are moved in equal time, through such-and-such an equal length, with respect to a change of the same kind.
lib. 7 l. 8 n. 2 Deinde cum dicit: si autem aliud etc., agit de comparatione motuum diversorum generum. Et dicit secundum praemissa, quod si unum mobile alteretur, aliud vero ducatur, idest secundum locum moveatur, numquid potest dici quod alteratio sit aeque velox loci mutationi? Sed hoc dicere esset inconveniens. Cuius causa est, quia motus habet diversas species, et iam dictum est quod ea quae non sunt unius speciei, non sunt comparabilia. Quia ergo loci mutatio non est eiusdem speciei cum alteratione, non sunt comparabiles velocitates alterationis et loci mutationis.	941. Then at (723 249 a12) he discusses the comparison of motions in diverse genera. And he asks, in keeping with what went before, “If one mobile be altered and another moved locally, can the alteration be said to be ‘as swift as’ the local motion?” To say “yes” would be unacceptable. The reason is that the two motions are of different species—and it has already been said that things not of the same species cannot be compared. Therefore, since local motion is not of the same species as alteration, the swiftness of the two cannot be compared.
lib. 7 l. 8 n. 3 Deinde cum dicit: quare si quae in aequali tempore etc., agit de comparatione motuum unius generis in uno genere. Et primo quantum ad loci mutationem; secundo quantum ad alterationem, ibi: de alteratione autem quomodo etc.; tertio quantum ad generationem et corruptionem, ibi: et in generatione autem et cetera. De augmento autem et diminutione mentionem non facit, quia eadem ratio est in his et in loci mutatione, cum sint et ipsi secundum aliquam magnitudinem. Circa primum tria facit: primo ostendit quid requiritur ad hoc quod duo motus locales sint ad invicem comparabiles; secundo excludit quoddam quod videbatur ad hoc requiri, ibi: aliquando autem in quo etc.; tertio concludit principale intentum, ibi: quare quae in aequali tempore et cetera. Circa primum duo facit: primo concludit inconveniens quod sequeretur si omnes loci mutationes essent comparabiles; secundo assignat causam quare non sint comparabiles, ibi: utrum ergo causa et cetera.	942. Then at (724 249 a13) he discusses the comparison of motions in some one species within some one genus. First as to change of place; Secondly, as to alteration, at 949; Thirdly, as to generation and ceasing-to-be, at 954. (He makes no mention of growth and decrease, because they share with local motion the common characteristic of being according to some magnitude,) In regard to the first he does three things: First he shows what is required in order that two local motions be able to be mutually compared; Secondly, he shows that one factor which seems to be required is not, at 945; Thirdly, he concludes to what he chiefly intended, at 946. About the first he does two things: First he concludes to the impossibility that would follow if all local motions could be compared; Secondly, he tells why not all can be compared$ at 944.
lib. 7 l. 8 n. 4 Dicit ergo primo, quod si aeque velocia sunt quae moventur localiter per aequalem magnitudinem in aequali tempore, et omnes loci mutationes contingit esse aeque veloces, sequetur quod sit aequalis rectus et circularis. Quod potest intelligi dupliciter: uno modo de motu recto et circulari; alio modo de linea recta et circulari; et hoc melius est, hoc enim sequitur ex eo quod praemisit. Si enim omnis motus rectus et circularis sunt aeque veloces; sunt autem aeque veloces motus, quando aequales magnitudines pertranseunt in aequali tempore; sequitur quod magnitudo recta et circularis sint aequales. Quod relinquitur pro inconvenienti.	943. He says therefore first (724 249 a13) that if the equally swift are things moved locally through an equal magnitude in equal time, and if all local motions should be equally swift, it would follow that what is straight is equal to what is circular. Now, this statement may be understood in two senses: first, in respect to a rectilinear motion and a circular one, secondly, in respect to a straight line and a circular one. The latter is the better sense, because it follows from the foregoing. For if all rectilinear and circular motions are equally swift-and they are so when they traverse an equal magnitude in equal time—it follows that a straight line is equal to a circular one, a situation that must be rejected as impossible.
lib. 7 l. 8 n. 5 Deinde cum dicit: utrum ergo causa etc., inquirit de causa incomparabilitatis motus recti et circularis. Quia enim concluserat quod si sunt aeque veloces, sequitur etiam magnitudines esse aequales, quod inconveniens videtur; posset aliquis dubitare utrum causa huius incomparabilitatis sit ex parte motus, vel ex parte magnitudinum. Et hoc est quod quaerit: utrum causa quare motus rectus non sit aeque velox motui circulari, sit quia loci mutatio est genus continens sub se diversas species (dictum est autem supra quod ea quae sunt diversa secundum speciem, non comparantur); aut causa eius est, quia linea est genus continens sub se rectum et circulare, sicut diversas species. Ex parte autem temporis non potest esse causa huius incomparabilitatis, quia omne tempus est atomus, idest indivisibile, secundum speciem. Huic ergo quaestioni respondet quod utrumque simul coniungitur; quia ex utraque parte invenitur differentia speciei: ita tamen quod diversitas speciei in loci mutatione causatur ex diversitate speciei in magnitudine super quam est motus. Et hoc est quod dicit, quod si illud super quod movetur, habet species, sequitur quod loci mutatio species habeat.	944. Then at (725 249 a14) he investigates the reason why rectilinear motions cannot be compared with circular ones. For since he had concluded that if they are equal, then the magnitudes are equal—which is seen to be impossible—someone might wonder whether the reason for this inability to be compared is due to the motion or to the magnitude. And this is his question: “Is the reason why a straight motion is not as equally swift as a circular one due to the fact that change of place is a genus containing diverse species under it (for it was said above that things of diverse species are not comparable), or is it because line is a genus containing under it straight and circular as species?” Of course, time cannot be the reason, for all time is “atomic,” i.e., indivisible, as to species. To this question. therefore, he responds that both reasons hold, because in both cases is found a difference of species, but in such a way, nevertheless, that the diversity of species it local motion is due to the diversity of species of the magnitudes in connection with which the motion takes place. And this is what he says, namely, that if that upon which the motion occurs has species, it follows that the local motion will have species.
lib. 7 l. 8 n. 6 Deinde cum dicit: aliquando autem in quo etc., excludit quoddam quod posset videri esse requirendum ad identitatem speciei et comparabilitatem in motibus localibus. Et dicit quod aliquando loci mutationes diversificantur secundum illud in quo, idest per quod sicut per instrumentum est loci mutatio; sicut si pedes sint quibus aliquid movetur, dicitur ambulatio; si autem sint alae, dicitur volatio. Sed hoc non facit diversitatem speciei in motibus localibus, sed figuris loci mutatio alia: idest, ista diversitas mutationum non est secundum speciem, sed solum secundum quandam figuram motus, ut Commentator exponit. Sed melius potest dici, quod hic intendit dicere quod loci mutatio specie non diversificatur per instrumenta motus, sed per figuras magnitudinis super quam transit motus: sic enim rectum et circulare differunt. Et ratio huius est, quia motus non recipiunt speciem a mobilibus, sed potius a rebus secundum quas mobilia moventur; instrumenta autem se tenent ex parte mobilium, figurae autem ex parte rei in qua est motus.	945. Then at (726 249 a16) he rejects a factor that might seem to be required for identity of species and comparability in local motions. And he says that sometimes changes of place are diversified by reason of “that in which,” i.e., by reason of that through which, as through an instrument, a local motion takes place; for example, if the feet are the instruments of local motion, it is walking, but if wings are, it is called flying. Yet this does not make for diversity of species in local motions but for a diversity of figure, as the Commentator says. However, it could possibly better be said that Aristotle here intends to say that changes of place are not diversified by reason of the instruments of motion but by reason of the figure of the magnitude traversed. For it is in this way that “straight” and “circular” differ. The reason is that motions are not diversified on account of the mobiles but on account of the things in respect to which the mobiles are moved. Now instruments lean more to the mobile, whereas figures are on the part of that in which the motion occurs.
lib. 7 l. 8 n. 7 Deinde cum dicit: quare quae in aequali tempore etc., concludit propositum. Et circa hoc tria facit: primo concludit principale propositum; secundo elicit quoddam consideratione dignum ex conclusione praemissa, ibi: et significat ratio haec etc.; tertio inquirit de diversitate speciei, ibi: quando igitur altera est species et cetera. Concludit ergo primo, quod ex quo motus non sunt comparabiles nisi sint unius speciei; et motus locales non sint unius speciei nisi sit eadem magnitudo secundum speciem: sequitur quod illa sint aeque velocia, quae moventur in aequali tempore secundum magnitudinem eandem: sed ita tamen, quod idem accipiatur quod est indifferens specie. Sic enim et motui conveniet quod sit indifferens specie. Et ideo hoc praecipue considerandum est in comparatione motuum, quae sit differentia motus: quia si est differentia genere vel specie, non sunt comparabiles; si autem est differentia secundum accidens, comparabiles sunt.	946. Then at (727 249 a19) he concludes his proposition. Concerning this he does three things: First he concludes to the main proposition; Secondly, he draws from the conclusion a fact to be considered, at 947; Thirdly, he investigates the problem of diversity of species, at 948. He concludes therefore first (727 249 a19) that since motions are not comparable unless they are of the same species, and local motions are not of one species unless they traverse the same specific magnitude, it follows that those are equally swift which traverse the same magnitude in equal time, where “same” refers to what is not different in species. For it is in this way that motions, too, do not differ in species, And therefore the main thing to be considered in the question of the comparison of motions is their differences. For if they differ either in genus or in species, they cannot be compared. But if they differ in accidentals, they can be.
lib. 7 l. 8 n. 8 Deinde cum dicit: et significat ratio haec etc., elicit ex praemissis quoddam consideratione dignum, scilicet quod genus non est aliquid unum simpliciter, species autem est aliquid unum simpliciter. Et hoc significatur ex ratione praecedenti, qua ostensum est quod ea quae sunt unius generis, non sunt comparabilia; quae vero sunt unius speciei, comparabilia sunt; cum tamen supra dictum sit, quod eadem natura comparabilium est: ex quo videtur quod genus non sit una natura, sed species sit una natura. Et huius ratio est, quia species sumitur a forma ultima, quae simpliciter una est in rerum natura: genus autem non sumitur a forma aliqua quae sit una in rerum natura, sed secundum rationem tantum; non est enim aliqua forma ex qua homo sit animal, praeter illam ex qua homo est homo. Omnes igitur homines, qui sunt unius speciei, conveniunt in forma quae constituit speciem, quia quilibet habet animam rationalem: sed non est in homine, equo aut asino aliqua anima communis, quae constituat animal, praeter illam animam quae constituit hominem vel equum aut asinum (quod si esset, tunc genus esset unum et comparabile, sicut et species); sed in sola consideratione accipitur forma generis, per abstractionem intellectus a differentiis. Sic igitur species est unum quid a forma una in rerum natura existente: genus autem non est unum; quia secundum diversas formas in rerum natura existentes, diversae species generis praedicationem suscipiunt. Et sic genus est unum logice, sed non physice. Quia ergo genus quodammodo est unum, et non simpliciter, iuxta genera latent multa: idest, per similitudinem et propinquitatem ad unitatem generis, multorum aequivocatio latet. Sunt autem quaedam aequivocationum multum distantes, in quibus sola communitas nominum attenditur; sicut si canis dicatur caeleste sidus, et animal latrabile. Quaedam vero sunt quae habent quandam similitudinem; sicut si hoc nomen homo dicatur de vero homine et de homine picto, inquantum habet similitudinem quandam veri hominis. Quaedam vero aequivocationes sunt proximae: aut propter convenientiam in genere (sicut si corpus dicatur de corpore caelesti et de corpore corruptibili, aequivoce dicitur, naturaliter loquendo, quia eorum non est materia una. Conveniunt tamen in genere logico: et propter hanc generis convenientiam videntur omnino non aequivoca esse): aut etiam sunt propinquae secundum aliquam similitudinem; sicut ille qui docet in scholis dicitur magister, et similiter ille qui praeest domui dicitur magister domus, aequivoce, et tamen propinqua aequivocatione propter similitudinem; uterque enim est rector, hic quidem scholarum, ille vero domus. Unde propter hanc propinquitatem vel generis vel similitudinis, non videntur esse aequivocationes, cum tamen sint.	947. Then at (728 249 a21) he draws from the foregoing a fact worthy of consideration, namely, that a genus is not something absolutely one, whereas a species is. This is made known first of all from the preceding argument in which it was shown that things not of one genus are not comparable, whereas things of one species are; and secondly, from the preceding lecture, in which it was stated that the nature of comparable things is one. From this it can be gathered that a genus is not one nature, while a species is. The reason for this is that the species is taken from the ultimate form, which is absolutely one in the universe of things, but the genus is not taken from a form that is one in the universe of things but from one that is so in conception only. For the form on account of which man is animal is not distinct from the one on account of which man is man. Therefore, all men who are of one species agree in the form which constitutes their species, because each has a rational soul. But there is not in man, horse, and ass, some common soul which makes them animal, over and above the soul that makes one a man, or a horse, or an ass. (If there were, then the genus would be one and comparable, just as the species.) But it is only in our mental consideration that a generic form is extracted, namely, it is brought about by the intellect’s abstracting from the differences. Consequently a species is one quiddity deriving from a unity of form existing in the universe of things. The genus, however, is not one, because according to the diverse forms existing in the universe of things, diverse species are capable of receiving a same genus as a predicate. Consequently, a genus is one thing logically but not physically. Now, because a genus, although not purely one, is still in some sense one, the equivocation of many things is often masked on account of their likeness and their closeness to a unity of genus. Now certain equivocal things are very unlike and possess in common only a name, as when a heavenly body, and the animal which barks, are called “dogs.” Other things, however, have a certain likeness, as when the word “man” is applied to a real man, and to one that is in a painting, on account of the latter’s likeness to a real man. Still other equivocations are very close. This may be on account of agreement in genus. For example, when “body” is said of a heavenly body and of a corruptible body, it is equivocation, because naturally speaking the matter is not one. They agree, however, in logical genus, for which reason they appear not to be equivocal. Or it may be on account of some likeness. For example, one who teaches in the schools is called “master.” and so is the head of a house, equivocally; this is by a close equivocation, however, on account of the likeness, for each is a ruler, one in the schools, the other in the house, Hence, on account of their close resemblance in genus or likeness things do not appear to be equivocal which nevertheless are.
lib. 7 l. 8 n. 9 Deinde cum dicit: quando igitur altera etc., quia dixerat quod considerandum est quae sit differentia motus, utrum scilicet motus differant specie; hic inquirit quomodo differentia speciei accipi possit, tam in motibus quam in aliis. Et quia essentiam speciei significat definitio, quaerit duas quaestiones: unam de specie, et aliam de definitione. Quaerit ergo primo de specie, quando sit iudicanda altera species: utrum ex hoc solo quod eadem natura sit in alio et alio susceptibili, sicut Platonici posuerunt. Sed hoc secundum praemissa non potest esse verum. Dictum est enim quod genus non est simpliciter unum: et ideo differentia speciei non attenditur per hoc quod aliquid idem sit in alio et alio, nisi secundum Platonicos, qui posuerunt genus esse simpliciter unum. Et propter hoc, quasi quaestionem solvens, subiungit: aut si aliud in alio; quasi dicat: non propter hoc est alia species, quia est idem in alio; sed quia est alia natura in alio susceptibili. Secundam quaestionem movet de definitione: et est quaestio quid sit terminus, idest, quae sit definitio declarans speciem. Et quia ea quae sunt idem definitione, sunt idem simpliciter, ideo quasi solvens subiungit, quod illud est propria definitio rei, quo possumus discernere utrum sit idem aut aliud, puta album vel dulce. Et hoc quod dico aliud, potest duobus modis accipi, sicut et prius: uno scilicet modo ut album dicatur aliud a dulci, quia in albo invenitur alia natura subiecta quam in dulci; alio modo, quia non solum secundum naturam subiectam differunt, sed omnino non sunt idem. Quae quidem duo sunt eadem cum his quae supra posuit: si idem in alio, aut si aliud in alio. Manifestum est enim quod eadem est ratio identitatis et diversitatis, et in specie et in definitione.	948. Then at (729 249 a25) because he had said that we must consider the question of the differences of motion, i.e., whether motions differ specifically, he now inquires how specific differences may be taken in motions and in other things as well. And because the definition designates the essence of the species, he poses two questions: one about the species, and one about the definition. He first of all asks about species: “When is something to be reckoned of a different species from another? Is it only because the same nature is found in different receivers, as Plato held?” According to the foregoing this cannot be the case. For it has been said that a genus is not absolutely one; therefore a difference of species is not reckoned on the basis that some same thing is in one and another, except for the Platonists who posited that a genus is absolutely one. On this account, as though answering the question, Aristotle adds that a species is different, not because the same thing is in a different subject, but because a different nature is in a different subject. The second question is about definition, and it is this: “What is a term, i.e., what is the definition which declares a species?” And because things that have the same definition are absolutely the same, he then, as if answering the question, adds that the proper definition of a thing is that by which we can discern whether some thing is the same or other, e.g. white or sweet. And “other” may be taken in two ways as before: in one way, as meaning that the white is said to be something other than the sweet, because in the white thing is found a subject nature other than the one in the sweet; in another way, as meaning that they differ not only in subject nature but that they are wholly not the same. These two are the same as the two he mentioned above, when he said: “If the same thing is found in things that are other, or if differing things are found in differing things.” For it is clear that there is a same reason of identity and diversity in species and in definition.
lib. 7 l. 8 n. 10 Deinde cum dicit: de alteratione autem etc., agit de comparatione alterationum. Et circa hoc duo facit: primo ostendit quod una alteratio est aeque velox alteri; secundo inquirit secundum quid aequalitas velocitatis attendatur in alteratione, ibi: sed quid alteratum est et cetera. Quaerit ergo primo de alteratione, quomodo sit una alteratio aequaliter velox alteri alterationi. Et quod duae alterationes sint aeque veloces, probat. Sanari enim est alterari: contingit autem unum cito sanari, et alium tarde; et contingit etiam quosdam simul sanari: ergo una alteratio est aeque velox alteri; illud enim dicitur aeque velociter moveri, quod in aequali tempore movetur.	949. Then at (730 249 a29) he discusses the comparison of alterations, About this he does two things: First he shows that one alteration is as equally fast as another; Secondly, he investigates from what aspect equality of quickness in alteration is considered, at 950. He asks therefore first about alteration, how one alteration is as equally fast as another. And that two alterations are equally fast, he proves. For being healed is to be altered. But one can be healed swiftly and another slowly, and likewise some come to be healed at the same time. Therefore, one alteration is as equally swift as another, for what is moved in an equal time is said to be moved with equal speed.
lib. 7 l. 8 n. 11 Deinde cum dicit: sed quid alteratum etc., quia in motu locali, ad hoc quod sit aequalis velocitas, requiritur non solum aequalitas temporis, sed etiam aequalitas magnitudinis quae pertransitur; supposito quod in alteratione aequalitas temporis requiratur ad aequalem velocitatem, inquirit quid aliud requiratur. Et hoc est quod dicit: sed quid alteratum est? Idest, quid est illud, ad quod cum pervenerit alteratio in aequali tempore, possit dici aeque velox? Et ratio dubitationis est, quia in qualitate, circa quam est alteratio, non invenitur aequale: ut possimus dicere quod quando pervenit ad aequalem quantitatem in aequali tempore, sit aeque velox alteratio; sicut dicebatur in motu locali, et etiam dici potest in augmento et diminutione. Sed sicut in quantitate invenitur aequalitas, ita et in qualitate invenitur similitudo. Huic ergo quaestioni respondet cum subdit: sed sit idem et cetera. Et primo ponit responsionem ad quaestionem: et dicit quod alteratio debet dici aeque velox, si in aequali tempore mutatum sit idem, idest illud quod est alteratum.	950. Then at (731 249 b2), because equality of speed in local motion requires not only equality of time but also of magnitude traversed, and assuming that in alteration equality of time is required for equality of speed, he asks what else is required. And this is what he says: “What is it that must be reached in equal time in order that an alteration be called equally swift?” And the reason for this question is that in quality, with which alteration is concerned, equal is not found, so as to enable us to say that when an equal quantity is reached in equal time there is an equally fast alteration, as indeed happens in local motion, as well as in growth and decrease. But as equality is found in quantity, likeness is found in quality. To this question he responds at (732 249 b4). And first he answers the question, and says that alterations should be called equally swift if in an equal time it is the same thing which has been changed, i.e., altered.
lib. 7 l. 8 n. 12 Secundo ibi: utrum ergo etc., movet quaestionem circa positam solutionem: et est quaestio quam primo movet, talis. Cum enim dictum sit quod aeque velox alteratio est, si sit idem quod alteratum est in aequali tempore; in eo autem quod est alteratum duo est considerare, scilicet passionem secundum quam fit alteratio, et subiectum in quo est passio: est ergo quaestio utrum huiusmodi comparationem oporteat accipere secundum identitatem passionis, an secundum identitatem subiecti in quo est passio.	951. Secondly, he raises a question about this answer. Since it has been said that there is an equally swift alteration, if it is the same thing that has been altered in an equal time, and since in that which has been altered there are two things to consider, namely, the quality with respect to which alteration occurred, and secondly, the subject in which the quality exists, the question arises: “Should a comparison of this sort be regarded from the viewpoint of the identity of the quality or of the identity of the subject in which the quality exists?”
lib. 7 l. 8 n. 13 Secundo ibi: hic igitur etc., solvit quaestionem quantum ad unam partem: et dicit quod in alteratione ex parte passionis duplex identitas attendi debet, ad hoc quod sit aeque velox alteratio. Primo quidem quod sit eadem qualitas secundum speciem: puta ut accipiatur eadem sanitas, ut oculi aut alicuius huiusmodi. Secundo ut eadem qualitas accepta similiter insit, neque magis neque minus. Sed si passio, idest passibilis qualitas, est altera secundum speciem, puta si unum alteratum fiat album et aliud sanetur; in his duabus passionibus nihil est idem, neque aequale, neque simile. Unde secundum diversitatem harum passionum fiunt diversae species alterationis, et non est una alteratio: sicut etiam supra dictum est, quod motus rectus et circularis non sunt una loci mutatio. Et ideo ad comparandum tam loci mutationes quam alterationes, considerandum est quot sint species alterationis vel loci mutationis, utrum scilicet eadem vel plures. Et hoc quidem potest considerari ex rebus in quibus est motus: quia si illa quae moventur, idest secundum quae est motus per se et non secundum accidens, differunt specie, et motus specie differunt; si vero differunt genere, et motus differunt genere; et si numero, et motus differunt numero, ut in quinto dictum est.	952. Then at (734 249 b6) he answers one part of the question and says that with respect to the quality received in alteration, two types of identity must be considered in order that alterations be equally swift. First, that the same specific quality be involved, for example, the same health, of the eye or of something similar; secondly, that the quality which is taken be present in the same way, and neither more nor less. But if the qualities in question differ specifically, e.g., if one alteration involves becoming white, and another healthy, in these two cases nothing is the same; they are neither equal nor alike. Hence a diversity of these qualities causes a diversity in species of alteration, so that the alterations are not one, just as it was said above that a straight motion and a circular one are not one local motion. Consequently, whenever you wish to compare either local motions or alterations, you have to consider the species of alterations or of local motion to see whether they are the same or many. And this may be considered from the things in which motions occur, for if the things which are moved, i.e., in which motion occurs per se, and not per accidens, differ specifically, then the motions differ specifically; if they differ generically, so do the motions differ generically; if they differ numerically, then also the motions differ numerically, as was pointed out in Book V.
lib. 7 l. 8 n. 14 Tertio ibi: sed utrum oporteat etc., determinata una parte quaestionis quam moverat, quaerit de alia. Et est quaestio utrum ad hoc quod iudicentur alterationes esse similes vel aeque veloces, oporteat respicere solum ad passionem, si sit eadem; aut etiam oporteat respicere ad subiectum quod alteratur; ita scilicet quod si huius corporis tanta pars sit albata in hoc tempore, et alterius corporis aequalis pars sit albata in eodem vel aequali tempore, dicatur alteratio aeque velox. Et solvit quod oportet ad utrumque respicere, scilicet ad passionem et subiectum: diversimode tamen. Quia iudicamus alterationem esse eandem vel aliam ex parte passionis, secundum quod est eadem vel alia: sed iudicamus alterationem aequalem vel inaequalem, secundum quod pars subiecti alterati est aequalis vel inaequalis: si enim huius corporis albetur magna pars, alterius autem parva, erit quidem alteratio eadem specie, sed non aequalis.	953. Thirdly, at (735 249 b14), having determined one part of the question he raised, he now attacks the other. The question is this: “In order that alterations be adjudged similar or equally swift should regard be paid only to the quality to see if it is the same, or also to the subject which is altered; that is, if a certain portion of this body becomes white in a certain time and an equal part of another becomes white in the same or in equal time, should the alterations be judged equally swift?” And he answers that attention must be paid to both, i.e., to the quality involved and to the subject, but in different ways. For from the viewpoint of the quality we judge an alteration to be the same or different according to whether the quality is the same or not; but we judge an alteration to be equal or unequal, if the part of the subject altered is equal or unequal: for if a large part of this body becomes white and a small part of another becomes white, the alterations will be specifically the same, but they will not be equal.
lib. 7 l. 8 n. 15 Deinde cum dicit: et in generatione etc., ostendit quomodo debeat fieri comparatio in generatione et corruptione. Et primo secundum opinionem propriam; secundo secundum opinionem Platonis, ibi: et si est numerus substantia et cetera. Dicit ergo primo, quod in generatione et corruptione, ad hoc quod generatio dicatur aeque velox, considerandum est si in aequali tempore sit idem quod generatur et indivisibile secundum speciem: puta si in utraque generatione generetur homo in aequali tempore, est aeque velox generatio. Sed non est aeque velox generatio ex hoc solo quod in aequali tempore generatur animal; quia quaedam animalia propter sui perfectionem indigent maiori tempore ad generationem: sed velocior dicitur esse generatio, si in aequali tempore generetur alterum; puta si in tanto tempore, in quo ex una parte generatur canis, ex alia parte generetur equus, esset equi velocior generatio. Et quia in alteratione ex parte passionis dixerat duo consideranda, scilicet si est eadem sanitas, et iterum si similiter existit et neque magis neque minus; hic autem in generatione unum tantum dixit considerandum, scilicet si sit idem quod generatur; huius modo causam assignat dicens: non enim habemus aliqua duo in quibus alteritas, sicut dissimilitudo. Quasi dicat: ideo in generatione hoc solum considerandum utrum sit idem quod generatur, quia in generatione non habemus aliquid quod possit variari per duo, secundum quae attendatur aliqua alteritas; sicut in alteratione accidit dissimilitudo per hoc quod una et eadem qualitas variatur secundum magis et minus: substantia enim, cuius est generari, non recipit magis et minus.	954. Then at (736 249 b19) he shows how comparison should be made with respect to generation and ceasing-to-be. First, according to his own opinion; Secondly, according to the opinion of Plato, at 955. He says therefore first (736 249 b19) that in generation and ceasing-to-be, in order that a generation be called equally swift, we must consider whether in an equal time the same thing is generated and is something indivisible as to species; for example, if a man is begotten in equal time in both generations, they are equally swift. But generations are not equally swift just because an animal is generated in equal time, for some animals on account of their perfection require more time for being generated~ But generation is said to be swifter, if something else is generated in an equal time; for example, if in the time required for the generation of a dog, a horse should be generated, the generation of the horse would be swifter. And because he had said that, in alteration, from the viewpoint of the quality involved, two things must be considered, namely, whether it is the same health and whether it exists in the same way and not more or less, while here he says that in generation only one thing has to be considered, namely, whether it is the same that is being generated, he now gives the reason for this difference, saying: “For we do not have two things in which there is an otherness called unlikeness.” It is as if he said: “The reason why in generation the only thing to be considered is whether it is the same that is being generated, is that in generation we do not have something that could vary with regard to two things, according to which a difference could be discerned, in the way that unlikeness occurs in alteration through the fact that one and the same quality can vary according to more and less. For a substance, which is the proper terminus of generation, is not capable of more and less.”
lib. 7 l. 8 n. 16 Deinde cum dicit: et si est numerus etc., agit de comparatione generationis secundum opinionem Platonis, qui ponebat numerum esse substantiam rei, propter hoc quod unum quod est principium numeri, putabat esse idem cum uno quod convertitur cum ente, et rei substantiam significat. Ipsum autem quod est unum, est omnino unius naturae et speciei. Si ergo numerus, qui nihil est aliud quam aggregatio unitatum, sit substantia rerum secundum Platonicos, sequetur quod dicetur quidem maior et minor numerus secundum diversam speciem quantitatis; sed tamen quantum ad substantiam erit similis speciei. Et inde est quod Plato posuit speciem, unum: contraria vero, per quae diversificantur res, magnum et parvum, quae sunt ex parte materiae. Et sic sequetur quod sicut una et eadem sanitas habet duo, inquantum recipit magis et minus; sic etiam et substantia, quae est numerus, cum sit unius speciei ex parte unitatis, habebit aliqua duo, inquantum est maior et minor numerus. Sed in substantia non est commune nomen positum, quod significet utrumque, idest diversitatem quae accidit ex maioritate et minoritate numeri; sicut in passionibus, cum passio plus inest, aut qualitercumque est excellens, dicitur magis, ut puta magis album vel magis sanum; in quantitate autem, cum fuerit excellens, dicitur maius, ut maius corpus aut maior superficies. Sic autem non habemus nomen positum, quo communiter significetur excellentia substantiae, quae est ex maioritate numeri, secundum Platonicos.	955. Then at (737 249 b23) he discusses the comparison of generations according to the opinion of Plato, who supposed that number is the substance of a thing. For he thought that the “one” which is the principle of number is the substance of a thing. Now what is “one” is entirely of one nature and species. Therefore, if number, which is nothing more than an aggregate of units, is, according to Plato, the substance of things, it follows that a number will be called larger or smaller according to the species of quantity, but yet as to substance it will be of like species. And hence it is that Plato declared that one is the species, but that the contraries through which things differ are “the large and the small,” which are considered from the side of the matter. Accordingly, it will follow that just as one and the same health has two aspects, inasmuch as it receives more and less, so also substance, which is number, since it is of the same species on account of unity, will have two aspects according as the number is larger or smaller. But in substance no general word exists to signify both, i.e., the diversity which arises from the largeness and smallness of number, whereas in qualities, when more of one is in a subject or when it is in any way outstanding, the quality is said to be “more”—for example, “more white” or “more healthy”, while in quantity, excellence is described as “greater,” as a “greater body” or a “greater surface.” But in this sense there is no common word to signify excellence in substance—which is due to the largeness of number, according to the Platonists.