2091. Et similiter pluralitas vel multitudo, secundum quod significat entia divisa, non determinatur ad aliquod genus. Secundum autem quod significat aliquid mensuratum, determinatur ad genus quantitatis, cuius species est numerus. Et ideo dicit quod numerus est pluralitas mensurata uno, et quod pluralitas est quasi genus numeri.
2091. And in a similar way, insofar as plurality or multitude signifies beings which are divided, it is not limited to any particular genus. But insofar as it signifies something measured, it is limited to the genus of quantity, of which number is a species. Hence he says that number is plurality measured by one, and that plurality is, in a sense, the genus of number.
2092. Et non dicit quod sit simpliciter genus; quia sicut ens genus non est, proprie loquendo, ita nec unum quod convertitur cum ente, nec pluralitas ei opposita. Sed est quasi genus, quia habet aliquid de ratione generis, inquantum est communis.
2092. He does not say that it is a genus in an unqualified sense, because, just as being is not a genus properly speaking, neither is the one which is interchangeable with being nor the plurality which is opposed to it. But it is, in some sense, a genus, because it contains something belonging to the notion of a genus inasmuch as it is common.
2093. Sic igitur accipiendo unum quod est principium numeri et habet rationem mensurae, et numerum qui est species quantitatis et est multitudo mensurata uno, opponuntur unum et multa, non ut contraria, ut supra dictum est de uno quod convertitur cum ente, et de pluralitate sibi opposita; sed opponuntur sicut aliqua eorum quae sunt ad aliquid, quorum scilicet unum dicitur relative, quia alterum refertur ad ipsum. Sic igitur opponitur unum et numerus, inquantum unum est mensura et numerus est mensurabilis.
2093. Therefore, when we take the one which is the principle of number and has the character of a measure, and number, which is a species of quantity and is the plurality measured by one, the one and the many are not opposed as contraries—as has already been stated above  of the one which is interchangeable with being and of the plurality which is opposed to it—but they are opposed in the same way as things that are relative, that is, those of which the term one is used relatively. Hence the one and number are opposed inasmuch as the one is a measure and number is something measurable.
2094. Et quia talis est natura horum relativorum quod unum potest esse sine altero, sed non e converso, ideo hoc invenitur in uno et numero, quia si est numerus, oportet quod sit unum. Sed non oportet quod ubicumque est unum, quod sit numerus. Quia si est aliquid indivisibile ut punctus, ibi est unum, et non numerus. In aliis vero relativis quorum utrumque secundum se dicitur ad aliquid, neutrum est sine reliquo. Non enim est sine servo dominus, nec servus sine domino.
2094. And because the nature of these relative things is such that one of them can exist without the other, but not the other way around, this is therefore found to apply in the case of the one and number. For wherever there is a number, the one must also exist, but wherever there is a one, there is not necessarily a number. For if something is indivisible, as a point, we find the one there, but not number. But in the case of other relative things, each of which is said to be relative to another, neither is without the other. For there is no master without a servant, and no servant without a master.
2095. Deinde cum dicit similiter autem manifestat similitudinem relationis scibilis ad scientiam et unius ad multa; dicens, quod cum scientia similiter secundum rei veritatem dicatur ad scibile sicut numerus ad unum, non similiter assignatur a quibusdam; quia videtur quibusdam, sicut Pythagoricis, sicut supra dictum est, quod scientia sit mensura et scibile mensuratum.
2095. But while (1057a7). Here he explains the similarity between the relation of the knowable object to knowledge and that of the one to the many. He says that, although knowledge is truly referred to the knowable object in the same way that number is referred to the one, or the unit, it is not considered to be similar by some thinkers. For, to some, the Protagoreans (as has been said above ), it seemed that knowledge is a measure, and that the knowable object is the thing measured.
Sed contrarium apparet. Dictum est enim quod, si est unum quod est mensura, non est necesse numerum esse qui est mensuratum, sed e converso. Videmus enim quod si est scientia, oportet scibile esse. Non autem oportet, si est aliquid scibile, quod sit eius scientia. Unde apparet quod magis scibile est sicut mensura et scientia sicut mensuratum. Quodam enim modo mensuratur scibili scientia, sicut numerus uno. Ex hoc enim vera scientia rei habetur, quod intellectus apprehendit rem sicuti est.
But just the opposite of this is true. For it has been pointed out that, if the one or unit (which is a measure) exists, it is not necessary that there should be a number which is measured, although the opposite of this is true. And if there is knowledge, obviously there must be a knowable object; but if there is some knowable object, it is not necessary that there should be knowledge of it. Hence it appears rather that the knowable object has the role of a measure, and knowledge the role something measured; for, in a sense, knowledge is measured by the knowable object, just as a number is measured by one. For true knowledge results from the intellect apprehending a thing as it is.
2096. Deinde cum dicit pluralitas autem ostendit quod pluralitas vel multitudo absoluta non opponitur pauco, dicens: dictum est quod pluralitas secundum quod est mensurata, opponitur uni ut mensurae, sed non est contraria pauco. Sed pauco, quod significat pluralitatem excessam, opponitur multum, quod significat pluralitatem excedentem. Similiter etiam pluralitas non uno modo opponitur uni, sed dupliciter.
2096. And plurality (1057a12). Then he shows that an absolute plurality or multitude is not opposed to a few. He says that it has been stated before that, insofar as a plurality is measured, it is opposed to the one as to a measure, but it is not opposed to a few. However, “much,” in the sense of a plurality which is excessive, is opposed to a “few” in the sense of a plurality which is exceeded. Similarly, a “plurality” is not opposed to one in a single way, but in two.
Uno modo, sicut supra dictum est, opponitur ei ut divisibile indivisibili. Et hoc si accipiatur communiter unum quod convertitur cum ente, et pluralitas ei correspondens.
First, it is opposed to it in the way mentioned above , as the divisible is opposed to the indivisible. This is the case if the one which is interchangeable with being and the plurality which is opposed to it are understood universally.
Alio modo opponitur pluralitas uni ut ad aliquid, sicut scientia ad scibile. Et hoc dico si accipiatur pluralitas quae est numerus, et unum quod habet rationem mensurae, et est principium numeri.
Second, plurality is opposed to the one as something relative, just as knowledge is opposed to its object. And this is the case, I say, if one understands the plurality which is number and the one which has the character of a measure and is the basis of number.
The nature of contraries
Quoniam autem contrariorum contingit medium esse aliquod, et quorumdam est, necesse ex contrariis esse.
And since there can be an intermediate between contraries, and some contraries admit of intermediates, intermediates must be composed of contraries.
Omnia namque media in eodem sunt genere, et quorum sunt media. Media enim haec dicimus, in quaecumque permutari prius est necesse quod permutatur,
For all intermediates and the things of which they are the intermediates belong to the same genus. For we call those things intermediates into which some thing undergoing change must first change.
ut ab hypate in netem, si transit per mediam rationem, veniet prius ad medios sonos.
For example, if someone should pass from the top-string note to the bottom-string note, assuming that the passage is made through the intervening register, he will first come to the intermediate sounds.
Et in coloribus, si veniet ex albo in nigrum, prius veniet ad puniceum et ad plumbeum quam ad nigrum.
And the same thing is true in the case of colors; for if one will pass from white to black, he will first come to purple and to gray before he comes to black.
Similiter autem et in aliis. Permutari vero ex alio genere in aliud genus non est, nisi secundum accidens, ut ex colore in figuram. Necesse est ergo media et quorum sunt media, in eodem genere esse.
It is similar in the case of other things. But it is not possible except accidentally for a change to take place from one genus to another—for example, from color to figure. Hence intermediates and the things of which they are the intermediates must belong to the same genus.
At vero omnia media sunt oppositorum quorumdam. Ex his enim solis secundum se est permutari. Quapropter impossibile est esse media non oppositorum: esset enim permutatio et non ex oppositis.
But all intermediates are intermediates between certain things that are opposed, for it is only from these that change in the strict sense can arise. And for this reason there cannot be intermediates between things that are not opposed, for otherwise there would be a change which is not from opposites.
Oppositorum enim contradictionis quidem medium non est. Haec enim est contradictio, oppositio eius cuicumque adest altera pars non habentis medium ullum.
For the opposites involved in contradiction admit of no intermediates, for this is what contradiction is: an opposition of which one or the other part applies to anything whatever and which does not have an intermediate.
Caeterorum vero, alia ad aliquid, alia ut privativa, alia contraria. Eorum vero quae ad aliquid, quaecumque non contraria, non habent media.
But of other opposites, some are relative, some privative, and some contrary. And between those terms that are relative and not contrary, there is no intermediate.
Causa vero, quia non in eodem genere sunt. Quid enim scientiae et scibilis medium? Sed magni et parvi.
The reason is that they do not belong to the same genus; for what is the intermediate between knowledge and the knowable object? There is an intermediate, however, between the large and the small.
Si vero sunt in eodem genere media (ut ostensum est) et media contrariorum, necesse ipsa componi ex his contrariis.
Now, if intermediates belong to the same genus, as we have shown (1057a19), and are intermediates between things that are contrary, they must be composed of these contraries.
Nam erit aut aliquid genus ipsorum, aut nullum. Et si quidem genus erit, ita ut sit prius aliquid contrariis, differentiae priores contrariae erunt facientes contrarias species, ut generis. Ex genere enim et differentiis, species. Ut si album et nigrum contraria: est autem hic quidem disgregativus color, ille vero congregativus color: hae differentiae congregativum et disgregativum priores. Quare haec contraria invicem priora. At vero contrariae differentiae, magis sunt contraria.
For there will be some genus of these contraries or there will not. And if there is some genus such that it is something prior to the contraries, there will be contrary differences prior to the species, constituting them as contrary species of the genus; for species are composed of genus and differences. Thus, if white and black are contraries, and the one is an expanding color and the other a gathering color, the differences “expanding” and “contracting” will be prior. Hence these things that are contrary to each other will be prior. But contrary differences are more truly contrary.
Et reliqua et media ex genere erunt et differentiis. Ut quicumque colores albi et nigri sunt medii, oportet hos ex genere dici (est autem genus color), et ex differentiis quibusdam. Haec vero non erunt prima contraria. Si autem non, erit unusquisque aut albus aut niger. Altera igitur media. Ergo primorum contrariorum hae erunt.
And the other species, the intermediate ones, will be composed of genus and differences. For example, all colors intermediate between white and black must be defined by a genus (which is color) and by differences. But these differences will not be the primary contraries; if this were not the case, every color would be either white or black. Hence the intermediate species are different from the primary contraries.
Primae autem differentiae congregativum et disgregativum, quia haec prima sunt. Quaerendum autem quaecumque contraria non in genere, ex quo media ipsorum.
And the primary differences will be “expanding” and “contracting,” because these are primary. Moreover, it is necessary to investigate those contraries which belong to the same genus and to discover the things of which their intermediates are composed.
Necesse enim quae sunt in eodem genere, ex incompositis genere componi, aut incomposita esse. Contraria namque incomposita sunt ex invicem, quare principia: quae autem sunt intermedia, aut omnia, aut nullum. Ex contrariis vero fit aliquid.
For things belonging to the same genus must either be composed of things that are incomposite in the same genus or be incomposite in themselves. For contraries are not composed of each other (and thus are principles), but either all or none of the intermediates are incomposite. But something comes about from contraries.
Quare erit transmutatio in hoc prius quam in ipsa; utriusque enim et minus erit et magis. Medium igitur erit et hoc contrariorum.
Hence change will affect this before reaching the contraries, for it will be less than one contrary and greater than the other, and thus this will be an intermediate between the contraries.
Et alia igitur omnia composita, quae sunt media. Nam huius quidem magis, istius vero minus compositum est aliqualiter ex illis quorum dicitur esse; huius quidem magis, illius vero minus.
All the other intermediates, then, are composites, for that intermediate which is greater than one contrary and less than the other is composed in a sense of these contraries of which it is said to be greater than one and less than the other.
Quoniam autem non sunt alia priora eiusdem generis contrariis, omnia utique ex contrariis media erunt. Quare et inferiora omnia et contraria et media, ex primis contrariis erunt.
And since there are no other things belonging to the same genus which are prior to the contraries, all intermediates will be composed of contraries. All inferiors, then, both contraries and intermediates, must be composed of the primary contraries.
Quod quidem igitur media et in eodem genere omnia, et intermedia contrariorum, et componuntur ex contrariis omnia palam.
Hence it is evident that all intermediates belong to the same genus, that they are intermediates between contraries, and that they are composed of contraries.
2097. Postquam Philosophus determinavit de contrariis, hic determinat de mediis contrariorum; et circa hoc duo facit.
2097. Having expressed his views about contraries, the Philosopher now does the same thing with regard to the intermediates between contraries; and concerning this, he does two things.
Primo proponit de quo est intentio; dicens: quia contrariorum contingit aliquid esse medium, ut supra dictum est, et quaedam contrariorum medium habent, ostendendum est quod necesse est media esse ex contrariis. Non autem hoc solum ostendit, sed etiam quaedam alia quae ad huius probationem sunt necessaria.
First (1057a18; ), he indicates what his plan is. He says that, since there can be an intermediate between contraries, as has been shown above (1055a38; ), and some contraries have an intermediate, it is necessary to show that intermediates are composed of contraries. He not only does this but also proves certain points needed for this proof.
Intermediaries of contraries
2098. Deinde cum dicit omnia namque prosequitur suam intentionem; et circa hoc tria facit.
2098. For all intermediates (1057a19). Then he carries out his plan, and in regard to this, he does three things.
Primo ostendit, quod media sunt in eodem genere cum contrariis.
First, he shows that intermediates belong to the same genus as contraries.
Secundo ostendit, quod media sunt inter contraria tantum, ibi, at vero media et cetera.
Second (1057a30; ), he shows that there are intermediates only between contraries, at but all intermediates.
Tertio vero ostendit, quod media componuntur ex contrariis, quod est principaliter intentum, ibi, si vero sunt in eodem genere.
Third (1057b2; ), he establishes his main thesis, that intermediates are composed of contraries, at now, if intermediates.