Authors/Thomas Aquinas/physics/L7/lect7

Lecture 7 The comparing of motions; what is required

Latin	English
	Lecture 7 The comparing of motions; what is required
lib. 7 l. 7 n. 1 Postquam philosophus ostendit quod in mobilibus et motoribus necesse est ponere aliquod primum; quia ea quae sunt unius ordinis videntur comparabilia esse, et hoc ipsum quod est prius et posterius comparationem importat, vult ex consequenti inquirere de motuum comparatione. Et circa hoc duo facit: primo enim ostendit qui motus sint comparabiles ad invicem; secundo qualiter motus ad invicem comparentur, ibi: quoniam autem movens movet et cetera. Circa primum tria facit: primo movet dubitationem; secundo obiicit ad partes dubitationis, ibi: si ergo cum in aequali etc.; tertio dubitationem solvit, ibi: sed quaecumque non aequivoca et cetera. Movet autem dubitationem primo quidem in communi, quaerens utrum omnis motus sit comparabilis cuilibet motui, vel non: deinde vero in speciali, dubitationem inferens primo quidem de motibus unius generis. Quia si omnis motus cuilibet motui sit comparabilis secundum velocitatem et tarditatem (dictum est autem in sexto quod aequaliter velox est, quod movetur in aequali tempore per aequale spatium), sequetur quod motus circularis sit aequalis recto et maior et minor in velocitate; et ulterius quod linea circularis sit aequalis lineae rectae in quantitate, aut maior et minor; ex quo aeque velox est quod per aequale movetur in aequali tempore. Deinde infert dubitationem de motibus diversorum generum. Si enim omnes motus comparabiles sunt in velocitate, sequetur quod si in aequali tempore hoc quidem alteretur, illud vero moveatur secundum locum, quod sit aequalis in velocitate alteratio loci mutationi. Et ulterius, per definitionem aeque velocis, sequetur quod passio, idest passibilis qualitas, secundum quam est alteratio, sit aequalis longitudini spatii, quae pertransitur per motum localem: quod est impossibile manifeste, quia non conveniunt in eadem ratione quantitatis.	928. After the Philosopher has shown that it is necessary to posit a first in mobiles and movers, now, because things which are of one order seem capable of being compared, and because to be “prior” and “subsequent” implies a comparison, he wishes to inquire about comparison of motions. Concerning this he does two things: First, he shows which motions can be mutually compared; Secondly, how motions are mutually compared, (L. 9). About the first he does three things: First, he raises a question; Secondly, he objects against both parts of the question, at 929; Thirdly, he settles the question, at 933. First he raises a general question (709 248 a10) and asks whether just any motion at random may be compared to just any other motion or not. Then he raises a special question about motions in some one genus. Now if any motion at random may be compared to just any other motion with respect to swiftness and slowness (it having been said in Book VI that the equally swift is what is moved in equal time over an equal space), it will follow that a circular motion will be equal, or greater, or less, in swiftness than a rectilinear one, and further, that a curved line will be equal to a straight line in quantity, or larger or smaller, from the fact that the equally swift is that which traverses an equal distance in equal time. Then he raises a question about motions in diverse genera. For if all motions may be compared with respect to speed, it will follow that if in an equal time A is altered, and B is moved locally, then a local motion is equal in swiftness to an alteration. Further, by virtue of the definition of the equally swift, it will follow that a passion, i.e., passible quality, in respect of which there is alteration, is equal to the length of the distance traversed by the local motion. But this is plainly impossibles because they do not agree in the same notion of quantity.
lib. 7 l. 7 n. 2 Deinde cum dicit: si ergo etc., obiicit ad propositam dubitationem: et primo quantum ad comparationem alterationis et loci mutationis; secundo quantum ad comparationem motus circularis et recti, ibi: in circulo autem et recto et cetera. Concludit ergo primo ex praemissa ratione ad impossibile ducente, contrarium posito; quasi dicat: dictum est quod inconveniens est passionem esse aequalem longitudini: sed tunc aliquid est aequaliter velox, cum in aequali tempore movetur per aequale: ergo, cum nulla passio sit aequalis longitudini, sequitur quod loci mutatio non est aequalis in velocitate alterationi, neque maior aut minor. Ex quo ulterius concludi poterit, quod non omnes motus sint comparabiles.	929. Then at (710 248 a15) he raises objections against the question proposed: First, he objects against comparing alteration with local motion; Secondly, against comparing circular motion with rectilinear, at 930. First (710 248 a15), therefore, from the foregoing argument which leads to an impossibility, he concludes to the contrary of what he posited, as though saying that, since it has been said that it is not feasible for a passion to be equal to a length, while whenever something is moved through an equal space in equal time, it is said to be equally swift, therefore, since no passion is equal to a length, it follows that a local motion is not equal in swiftness to an alteration, or greater or less. From this it may be further concluded that not all motions can be compared.
lib. 7 l. 7 n. 3 Deinde cum dicit: in circulo autem etc., prosequitur quantum ad aliam partem dubitationis, scilicet de motu circulari et recto. Et primo obiicit ad hoc quod motus circularis sit aeque velox motui recto; secundo obiicit in contrarium, ibi: at vero si sunt comparabilia et cetera. Circa primum duo facit: primo obiicit ad propositum; secundo excludit cavillosam responsionem, ibi: amplius nihil differt et cetera. Obiicit autem primo sic. Motus circularis et rectus sunt differentiae motus localis, sicut et motus sursum et deorsum. Sed statim necesse est quod aliquid velocius aut tardius moveatur, si unum movetur sursum, aliud deorsum; vel etiam si idem quandoque movetur sursum, quandoque deorsum. Videtur ergo quod similiter oporteat dicere quod motus rectus sit velocior aut tardior circulari; sive idem sit quod movetur circulariter et recte, sive aliud et aliud. Est autem considerandum quod in hac ratione non facit mentionem de aeque veloci, sed de velociori et tardiori, quia haec ratio sumitur ex similitudine motus qui est sursum, cuius principium est levitas, et motus qui est deorsum, cuius principium est gravitas; quidam autem existimaverunt gravitatem et levitatem idem esse velocitati et tarditati (quod in quinto removit).	930. Then at (711 248 a18) he considers the other part of the question, i.e., concerning circular and rectilinear motion. First he objects against a circular motion’s being as equally swift as a rectilinear motion; Secondly, he takes the contrary position, at 932. About the first he does two things: First he objects against the proposition; Secondly, he dismisses a quibbling response, at 931. He objects first (71 248 a181) in the following manner. Circular motion and rectilinear are differences of local motion, just as upward and downward are. But as soon as something is moved upwards and something else downwards, it is at once necessary that one be being moved faster or slower than the other—the same is true if the same thing is moved now upwards and later downwards. It seems therefore that in like manner we must say that a rectilinear motion is swifter or slower than a circular one, whether it be the same thing that is being moved in a straight line and in a circular one, or two different things. It should be noted that in this argument he makes no mention of the equally swift but of the swifter and slower, because this argument is based on the likeness of an upward motion—whose principle is lightness—to a motion which is downward—whose principle is heaviness. Some, indeed, have held that heaviness and lightness are the same as swiftness and slowness—an opinion he rejected in Book V.
lib. 7 l. 7 n. 4 Deinde cum dicit: amplius nihil differt etc., excludit quandam cavillosam obviationem. Posset enim aliquis propter rationem praemissam concedere quod motus circularis esset aut velocior aut tardior quam rectus, non autem aeque velox. Et hoc excludit, dicens quod nihil differt quantum ad praesentem rationem, si aliquis dicat quod necessarium est quod id quod movetur circulariter, moveatur velocius aut tardius quam id quod movetur recte; quia secundum hoc motus circularis erit maior vel minor in velocitate quam rectus; unde sequitur quod etiam esse possit aequalis. Et quod hoc sequatur manifestat sic. Sit a tempus in quo aliquid velocius motum pertranseat ipsum b, qui est circulus: aliud autem tardius in eodem tempore pertranseat ipsum c, quod est recta linea. Quia ergo velocius in eodem tempore pertransit maius, sequetur quod b circulus sit aliquid maius quam c linea recta: sic enim supra in sexto definivimus velocius. Sed ibidem etiam diximus quod velocius in minori tempore pertransit aequale. Ergo erit accipere aliquam partem huius temporis quod est a, in qua corpus quod circulariter movetur, pertransibit aliquam partem huius circuli quod est b, et in eadem parte temporis pertransibit ipsum c; cum tamen corpus tardius in toto a tempore pertransiret totum c. Sequetur ergo quod illa pars circuli sit aequalis toti c, quia idem pertransit aequale in aequali tempore. Et sic linea circularis erit aequalis rectae, et motus circularis per consequens aeque velox recto.	931. Then at (712 248 a22) he rejects a quibble. For someone could concede on account of the foregoing reason that a circular motion is either swifter or slower than a rectilinear ones but not equally swift. This he rejects, saying that it makes no difference, so far as the present discussion is concerned, once someone grants that it is necessary for what is being moved circularly to be moved more swiftly or more slowly than what is being moved in a straight line. For according to this the circular motion will be faster or slower than the rectilinear. Hence it follows that it could also be equal. That this follows he now proves. Let A be the time in which the swifter traverses B, which is a circles and let something slower traverse the straight line C in the same time. Now, since the swifter traverses more in the same time, it will follow that circle B is larger than the straight line—that is the way the swifter was defined in Book VI. But we also said in that place that the swifter traverses an equal distance in less time. Therefore, we can take of time A a part during which the circularly moving body will traverse a part of this circle B and during which it will traverse C, while the slower body is traversing C in the entire time A. It will follow, therefore, that that part of the circle is equal to the entire C, because one and the same object traverses an equal distance in equal time. And in this way, a circular line will be equal to a straight line and a circular motion will, consequently, be as fast as a rectilinear.
lib. 7 l. 7 n. 5 Deinde cum dicit: at vero si sunt comparabilia etc., obiicit in contrarium. Quia si motus circularis et rectus sunt comparabiles in velocitate, sequitur quod modo dictum est, scilicet quod linea recta sit aequalis circulo, propter hoc quod aeque velox est quod per aequale movetur. Sed linea circularis et linea recta non sunt comparabiles, ut possint dici aequales: ergo neque motus circularis et rectus possunt dici aeque veloces.	932. Then (713 248 b4) he takes the contrary position. For if circular and rectilinear motions may be compared with respect to swiftness, it follows, as just said, that a straight line will be equal to a circular one, for the equally swift is what traverses an equal distance. But a circular line and a straight line cannot be compared, so as to be called equal. Therefore, neither can a circular motion be said to be as swift as a rectilinear.
lib. 7 l. 7 n. 6 Deinde cum dicit: sed quaecumque non aequivoca etc., solvit propositam dubitationem. Et primo inquirit in communi quid cui sit comparabile; secundo adaptat ad propositum, ibi: sic et circa motum et cetera. Circa primum tria facit: primo ponit unum quod requiritur ad comparationem; secundo secundum, ibi: aut quia sunt in alio etc.; tertio concludit tertium, ibi: sic ergo non solum oportet et cetera. Circa primum tria facit: primo ponit quid requiratur ad comparationem; secundo obiicit in contrarium, ibi: aut primum quidem etc.; tertio solvit, ibi: aut et in his eadem ratio et cetera.	933. Then at (714 248 b6) he settles the difficulty he raised. First he asks in general what may be compared to what; Secondly, he adapts this to his proposition, (L. 8). About the first he does three things: First he states one thing that is required for comparison; Secondly, a second thing, at 937. Thirdly, he concludes a third requirement, (at 939) About the first he does three things: First he mentions what is required for comparisons; Secondly, he takes the contrary position, at 935; Thirdly, he settles the matter, at 936.
lib. 7 l. 7 n. 7 Dicit ergo primo, quod quaecumque non sunt aequivoca, videntur esse comparabilia; ita scilicet quod secundum ea quae non aequivoce praedicantur, possint ea de quibus praedicantur, ad invicem comparari. Sicut acutum aequivoce sumitur: uno enim modo dicitur in magnitudinibus, secundum quem modum angulus dicitur acutus, et stylus acutus; alio modo dicitur in saporibus, secundum quem modum vinum dicitur acutum; tertio modo dicitur in vocibus, secundum quem modum vox ultima, idest suprema, in melodiis, vel chorda in cythara dicitur acuta. Ideo ergo non potest fieri comparatio ut dicatur quid sit acutius, utrum stylus aut vinum aut vox ultima, quia acutum de eis aequivoce praedicatur: sed vox ultima potest comparari secundum acuitatem, ei quae est iuxta ipsam in ordine melodiae, propter hoc quod acutum non aequivoce, sed secundum eandem rationem praedicatur de utraque. Secundum hoc ergo poterit dici ad propositam quaestionem, quod ideo motus rectus et circularis non comparantur in velocitate, quia velox aequivoce dicitur hic et ibi. Et multo minus est eadem ratio velocis in alteratione et loci mutatione: unde etiam haec multo minus comparabilia sunt.	934. He says therefore first (714 248 b6) that things seem to be capable of being compared so long as they are not equivocal, that is, in the line of things not predicated equivocally the subjects of predication may be compared. For example, “sharp” is an equivocal term: for in one sense it is applied to magnitudes, as when an angle is said to be “sharp” (acute) and when a pen-point is said to be “sharp”; in another sense it is applied to savors, as when wine is said to be “sharp” (dry); in a third sense it is applied to notes, as when the ultimate, i.e., highest, note in a melody, or a chord of a lyre is said to be “sharp.” Now, the reason why no answer can be made to the question, “Which of these is sharpest, the point, the wine or the voice?” is because “sharp” is predicated of them in an equivocal sense. But the highest note can be compared with respect to sharpness to another which is next to it in the scale, because in this case “sharp” is not taken equivocally, but is predicated of both in the same sense. Therefore, according to this, it could be replied to the proposed difficulty that the reason why a straight motion cannot be compared to a circular one is because the word “swift” is being used equivocally. And much less is the meaning of “swift” the same in respect to alteration and local motion. Consequently, these two are even less capable of being compared.
lib. 7 l. 7 n. 8 Deinde cum dicit: aut primum quidem etc., obiicit contra id quod dictum est. Et dicit quod quantum ad primum aspectum hoc non videtur esse verum, quod si aliqua non sunt aequivoca, quod sint comparabilia. Inveniuntur enim aliqua non aequivoca, quae tamen non sunt comparabilia; sicut hoc ipsum quod est multum, secundum eandem rationem dicitur de aqua et de aere, et tamen non sunt comparabilia aer et aqua secundum multitudinem. Si autem non velit aliquis hoc concedere quod multum idem significet propter eius communitatem, saltem concedet quod duplum, quod est species multiplicis, idem significat in aere et aqua: utrobique enim significat proportionem duorum ad unum. Et tamen non sunt comparabilia aer et aqua secundum duplum et dimidium, ut dicatur quod aqua est duplum aeris, aut e converso.	935. Then at (715 248 b12) he objects against what was just said. And he says that at first sight it does not seem to be true that things may be compared so long as they are not equivocal. For there are some non-equivocal things which cannot be compared; for example, “much” is used in the same sense when applied to water and to air, yet water and air cannot be compared with respect to muchness. Now if someone refuses to admit that “much” signifies the same thing on account of its general nature, he will at least grant that “double,” i.e., twice as much as, which is a species of muchness, signifies the same thing in regard to air and to water; for in both cases it signifies the ratio of 2 to 1. Nevertheless, air and water cannot be compared in terms of double and half, so as to be able to say that the amount of water is double that of the air or vice versa.
lib. 7 l. 7 n. 9 Deinde cum dicit: aut et in his eadem ratio etc., solvit propositam obiectionem. Et circa hoc duo facit: primo ponit solutionem; secundo confirmat eam, quandam quaestionem movendo, ibi: quoniam propter quid et cetera. Dicit ergo primo, quod potest dici quod in multo et duplo est eadem ratio quare non sunt comparabilia secundum quod dicuntur de aqua et aere, quae dicta est de acuto, secundum quod dicitur de stylo, vino et voce; quia etiam hoc ipsum quod est multum, aequivocum est. Et quia posset aliquis contra hoc obiicere ex hoc quod est eadem ratio multi secundum quod dicitur de utroque, ad hoc excludendum subiungit quod etiam rationes, idest definitiones, quorundam sunt aequivocae: sicut si dicat aliquis quod definitio multi est quod est tantum et adhuc amplius, hoc ipsum quod est tantundem et aequale, quod idem est, aequivocum est; quia aequale est quod habet unam quantitatem, non est autem eadem ratio unius quantitatis in omnibus. Ponitur autem hic ratio multi secundum quod multum importat comparationem, prout opponitur pauco; et non secundum quod accipitur absolute, prout opponitur uni. Et quod dixerat de multo, dicit consequenter de duplo. Quamvis enim ratio dupli sit, quod est proportio duorum ad unum, tamen ista etiam ratio continet aequivocationem: quia forte potest dici quod ipsum unum est aequivocum; et si unum aequivoce dicitur, sequitur quod duo, quia duo nihil aliud est quam bis unum. Est autem considerandum, quod multa quidem secundum abstractam considerationem vel logici vel mathematici non sunt aequivoca, quae tamen secundum concretam rationem naturalis ad materiam applicantis, aequivoce quodammodo dicuntur, quia non secundum eandem rationem in qualibet materia recipiuntur: sicut quantitatem et unitatem, quae est principium numeri, non secundum eandem rationem contingit invenire in corporibus caelestibus et in igne et in aere et aqua.	936. Then at (716 248 b15) he answers this objection. About this he does two things: First he gives the solution; Secondly, he confirms it by raising another question, at 937. He says therefore first that it could be said that in “much” and “double” we discern the same reason for their inability to be compared, when they are applied to water and to air, as was discerned in “sharp” when it was applied to pen and wine and note; for “much” itself is equivocal. Now, because someone could object against this on the ground that the same notion of “much” is referred to when it is applied to both, then in order to reject this, he states that even the notions, i.e., definitions, of certain things are equivocal. For example, if someone should say that the definition of “much” is that it is “this amount and yet more,” “to be this amount” and “to be equal,” which is the same thing, is equivocal, for “to be equal” is to have one quantity, but the definition of “one quantity” is not the same in all things. (The notion of “much,” as used here, implies a comparison in the sense that it is the opposite of “a little,” i.e., it is not taken in its absolute sense of being the opposite of “one.”) And what he said of “much” he says consequently of “double.” For although the notion of “double” is that there is a ratio of 2 to 1, yet even that notion contains an equivocation, for it could be said that “one” is equivocal; and if “one” is equivocal, it follows that “two” is, because “two” is nothing more than “one” taken twice. Now it should be observed that there are many things which, when considered in an abstract way in logic or mathematics, are not equivocal, but which are in a certain sense equivocal when they are taken in a concrete way, as the philosopher of nature takes them when he applies them to matter, for they are not taken according to the same aspect in all matter. For example, quantity, and unity (which is the principle of number) are not found according to the same aspect in the heavenly bodies, and in fire and air and water.
lib. 7 l. 7 n. 10 Deinde cum dicit: quoniam propter quid etc., confirmat quod dictum est, movendo quandam quaestionem. Si enim dicatur quod sit una natura multi et dupli et aliorum huiusmodi, quae non sunt comparabilia, sicut eorum quae univoce praedicantur; remanet quaestio quare quaedam quae habent unam naturam, sunt comparabilia, quaedam vero non sunt comparabilia. Videtur enim quod de similibus debeat esse idem iudicium. Deinde cum dicit: aut quia sunt in alio etc., respondet ad quaestionem motam, ponendo secundum quod ad comparationem requiritur. Et circa hoc duo facit: primo ponit secundum quod requiritur ad comparationem; secundo ostendit quod nec istud sufficit, ibi: aut manifestum est et cetera. Dicit ergo primo, quod ista potest esse ratio quare quaedam quorum est una natura, sunt comparabilia, quaedam vero non: quia si una natura recipiatur in diversis secundum unum primum subiectum, erunt illa ad invicem comparabilia; sicut equus et canis comparari possunt secundum albedinem, ut dicatur quod eorum sit albius, quia non solum est eadem natura albedinis in utroque, sed etiam est unum primum subiectum in quo recipitur albedo, scilicet superficies. Et similiter magnitudo est comparabilis in utroque, ut dicatur quod eorum sit maius; quia idem est subiectum magnitudinis in utroque, scilicet substantia corporis mixti. Sed aqua et vox non sunt comparabilia secundum magnitudinem, ut dicatur quod vox est maior quam aqua, aut e converso; quia licet magnitudo secundum se sit eadem, non tamen est idem receptivum: quia secundum quod dicitur de aqua, subiectum eius est substantia; secundum autem quod dicitur de voce, subiectum eius est sonus, qui est qualitas.	937. Then at (717 248 b21) he confirms what has been said by raising a certain other question. For if it be held that there is one nature of “much” and of “double” and of other like things which cannot be compared, as there is also one nature of things that are predicated univocally, the question still remains, why it is that among things having one nature some can be compared and some not. For it seems that when things are similar, there should be a same judgment about them. Then at (718 248 b22) he answers this question by positing the second requirement for things to be compared. About this he does two things: First he mentions the second requirement; Secondly, he shows that even that one is not enough, at 938. He says therefore first (718 248 b22) that the reason why some things possessing one nature can be compared, while other things having one nature cannot, could be that when some one nature is received according to one first subject in diverse things, they will be comparable, as horse and dog can be compared with respect to whiteness, one being able to be said “whiter” than the other, because not only is the same nature of whiteness in both, but there is one first subject in which whiteness is received, namely, the surface. In like manner, the magnitude of each may be compared, so that one can be called “larger” than the other, because there is one same subject of magnitude in each, namely, the substance of a mixed body. But water and a note cannot be compared with respect to magnitude so as to say that the note is “greater” than the water or vice versa, because although magnitude in itself is the same, the receiver of it is not the same. For when magnitude is said of water, its subject is a substance, but when it is said of a note, its subject is sound, which is a quality.
lib. 7 l. 7 n. 11 Deinde cum dicit: aut manifestum est etc., ostendit quod nec hoc sufficit, duabus rationibus. Quarum prima est: si propter hoc solum aliqua essent comparabilia, quia est subiectum non differens, sequeretur quod omnia haberent unam naturam; quia de quibuscumque diversis posset dici, quod non differunt nisi quia sunt in alio et alio subiecto primo. Et secundum hoc sequeretur quod hoc ipsum quod est aequale, et quod est dulce, et quod est album, esset una et eadem natura; sed differret solum per hoc quod est in alio et alio receptivo. Et hoc videtur inconveniens, quod omnia habeant unam naturam. Est autem considerandum, quod ponere diversitatem rerum propter diversitatem susceptivi tantum, est opinio Platonica, quae posuit unum ex parte formae, et dualitatem ex parte materiae; ut tota diversitatis ratio ex materiali principio proveniret. Unde et unum et ens posuit univoce dici, et unam significare naturam: sed secundum diversitatem susceptivorum, rerum species diversificari. Secunda ratio, quam ponit ibi: amplius susceptivum etc., est quod non quodlibet est susceptivum cuiuslibet; sed unum est primo susceptivum unius; et sic forma et susceptivum ad invicem dicuntur. Si ergo sunt plura prima susceptiva, necesse est quod sint plures naturae susceptae: aut si est una natura suscepta, necesse est quod sit unum primum susceptivum.	938. Then at (719 248 b25) he shows that this second requirement does not complete the list of requirements, for two reasons. The first of these is this: If things were comparable just because there is a non-differing subject, it would follow that all things have one nature, for it could be said of all things whatsoever that they do not differ except insofar as they exist in some one or other first subject. And according to this, it would follow that “to be equal” and “to be sweet” and “to be white” are one and the same nature, differing only by reason of being received in one or another receiver. And this is seen to be unacceptable, namely, that all things have one nature. But it should be noted that positing a diversity of things on the sole ground of diversity of subject is a Platonist opinion, which attributed unity to form and duality to matter, so that the entire reason of diversity came from the material principle. That was why he stated that “one” and “being” are predicated univocally, and that they signify one nature but that the species of things are diversified by reason of a diversity of receivers. The second reason which he gives, at (720 249 a2), is that not just anything is capable of receiving just anything else at random, but one is primarily the receiver of one; consequently, the form and what receives it are in proportion. Therefore, if there are many first receivers, there must necessarily be many natures capable of being received; or if one nature has been received, then necessarily there is one first receiver.
lib. 7 l. 7 n. 12 Deinde cum dicit: sic ergo non solum etc., concludit quod requiritur tertium ad hoc quod aliqua sint comparabilia. Et dicit quod oportet ea quae sunt comparabilia, non solum non esse aequivoca, quod erat primum; sed etiam non habere differentiam, neque ex parte subiecti primi in quo aliquid recipitur, quod erat secundum; neque ex parte eius quod recipitur, quod est forma vel natura; et hoc est tertium. Et exemplificat de hoc tertio. Quia color dividitur in diversas species coloris: unde non est comparabile secundum quod de eis praedicatur; licet non dicatur aequivoce, et licet etiam habeat unum primum subiectum, quod est superficies, quod est primum subiectum generis, non autem alicuius speciei coloris. Non enim possumus dicere quid sit magis coloratum, utrum album vel nigrum: haec enim comparatio non esset secundum aliquam determinatam speciem coloris, sed secundum ipsum colorem communem. Secundum vero album, quod non dividitur in diversas species, potest fieri comparatio omnium alborum, ut dicatur quid sit albius.	939. Then at (721 249 a3) he concludes that there is a third requirement for things to be comparable. And he says that things which can be compared must be not only non-equivocal (which is the first requirement) but must also not possess any difference either on the side of the first subject in which something is received (which is the second requirement) or on the side of what is received, which is a form or a nature (and this is the third). And he gives examples of this third requirement. For “color” is divided into various species of color; hence it cannot be compared solely on the ground that it is predicated of these colors, even though it be not predicated equivocally, and even though it have one first subject, which is a surface, and which is a first subject of the genus “color”, but not of any species of color. For we cannot say which is more colored, white or black, because this comparison would not be in terms of some definite species of color, but in terms of color in general. But in terms of whiteness, which is not divided into various species, all white things may be compared, so that it can be said which one is whiter.