Authors/Thomas Aquinas/metaphysics/liber5/lect17

Lecture 17

Latin	English
lib. 5 l. 17 n. 1 Hic determinat philosophus de ad aliquid: et circa hoc duo facit. Primo ponit modos eorum, quae sunt ad aliquid secundum se. Secundo eorum, quae sunt ad aliquid ratione alterius, ibi, illa vero quia sua genera. Circa primum duo facit. Primo enumerat modos eorum, quae secundum se ad aliquid dicuntur. Secundo prosequitur de eis, ibi, dicuntur autem prima. Ponit ergo tres modos eorum, quae ad aliquid dicuntur: quorum primus est secundum numerum et quantitatem, sicut duplum ad dimidium, et triplum ad tertiam partem, et multiplicatum, idest multiplex, ad partem multiplicati, idest ad submultiplex, et continens ad contentum. Accipitur autem continens pro eo, quod excedit secundum quantitatem. Omne enim excedens secundum quantitatem continet in se illud quod exceditur. Est enim hoc et adhuc amplius; sicut quinque continet in se quatuor, et tricubitum continet in se bicubitum.	1001. Here the Philosopher establishes the meaning of the relative or relation; and in regard to this he does two things. First, he gives the senses in which things are said to be relative directly; and second (1030), those in which things are said to be relative indirectly (“And other things”). In regard to the first he does two things. First, he enumerates the senses in which things are said to be relative directly. Second (1006), he proceeds to deal with these (“The first things”). He accordingly gives, first, three senses in which things are said to be relative directly. The first of these has to do with number and quantity as double to half and triple to a third, and “what is multiplied,” i.e., the multiple, to a part “of what is multiplied,” i.e., the submultiple, “and what includes to what is included in it.” But what includes is here taken for what is greater in quantity. For everything which is greater in quantity includes within itself that which it exceeds. For it is this and something more; for example, five includes within itself four, and three cubits include two.
lib. 5 l. 17 n. 2 Secundus modus est prout aliqua dicuntur ad aliquid secundum actionem et passionem, vel potentiam activam et passivam; sicut calefactivum ad calefactibile, quod pertinet ad actiones naturales, et sectivum ad sectibile, quod pertinet ad actiones artificiales, et universaliter omne activum ad passivum.	1002. The second sense is that in which some things are said to be relative according to acting and undergoing, or to active and passive potency; for example, in the realm of natural actions, as what can heat to what can be heated; and in the realm of artificial actions, as what can cut to what can be cut; and in general as everything active to everything passive.
lib. 5 l. 17 n. 3 Tertius modus est secundum quod mensurabile dicitur ad mensuram. Accipitur autem hic mensura et mensurabile non secundum quantitatem (hoc enim ad primum modum pertinet, in quo utrumque ad utrumque dicitur: nam duplum dicitur ad dimidium, et dimidium ad duplum), sed secundum mensurationem esse et veritatis. Veritas enim scientiae mensuratur a scibili. Ex eo enim quod res est vel non est, oratio scita vera vel falsa est, et non e converso. Et similiter est de sensibili et sensu. Et propter hoc non mutuo dicuntur mensura ad mensurabile et e converso, sicut in aliis modis, sed solum mensurabile ad mensuram. Et similiter etiam imago dicitur ad id cuius est imago, tamquam mensurabile ad mensuram. Veritas enim imaginis mensuratur ex re cuius est imago.	1003. The third sense of relation is that in which something measurable is said to be relative to a measure. Here measure and measurable are not taken (-) quantitatively (for this pertains to the first sense, in which either one is said to be relative to the other, since double is said to be relative to half and half to double), but (+) according to the measurement of being and truth. For the truth of knowledge is measured by the knowable object. For it is because a thing is so or is not so that a statement is known to be true or false, and not the reverse. The same thing applies in the case of a sensible object and sensation. And for this reason a measure and what is measurable are not said to be related to each other reciprocally, as in the other senses, but only what is measurable is related to its measure. And in a similar fashion too an image is related to that of which it is the image as what is measurable is related to its measure. For the truth of an image is measured by the thing whose image it is.
lib. 5 l. 17 n. 4 Ratio autem istorum modorum haec est. Cum enim relatio, quae est in rebus, consistat in ordine quodam unius rei ad aliam, oportet tot modis huiusmodi relationes esse, quot modis contingit unam rem ad aliam ordinari. Ordinatur autem una res ad aliam, vel secundum esse, prout esse unius rei dependet ab alia, et sic est tertius modus. Vel secundum virtutem activam et passivam, secundum quod una res ab alia recipit, vel alteri confert aliquid; et sic est secundus modus. Vel secundum quod quantitas unius rei potest mensurari per aliam; et sic est primus modus.	1004. These senses are explained as follows: since a real relation consists in the bearing of one thing upon another, there must be as many relations of this kind as there are ways in which one thing can bear upon another. (3) Now one thing bears upon another either in being, inasmuch as the being of one thing depends on another, and then we have the third sense; or (2) according to active or passive power, inasmuch as one thing receives something from another or confers it upon the other, and then we have the second sense; or (1) according as the quantity of one thing can be measured by another, and then we have the first sense.
lib. 5 l. 17 n. 5 Qualitas autem rei, inquantum huiusmodi, non respicit nisi subiectum in quo est. Unde secundum ipsam una res non ordinatur ad aliam, nisi secundum quod qualitas accipit rationem potentiae passivae vel activae, prout est principium actionis vel passionis. Vel ratione quantitatis, vel alicuius ad quantitatem pertinentis; sicut dicitur aliquid albius alio, vel sicut dicitur simile, quod habet unam aliquam qualitatem. Alia vero genera magis consequuntur relationem, quam possint relationem causare. Nam quando consistit in aliquali relatione ad tempus. Ubi vero, ad locum. Positio autem ordinem partium importat. Habitus autem relationem habentis ad habitum.	1005. But the quality as such of a thing pertains only to the subject in which it exists, and therefore from the viewpoint of quality one thing bears upon another only inasmuch as quality has the character of an active or passive power, which is a principle of action or of being acted upon. Or it is related by reason of quantity or of something pertaining to quantity; as one thing is said to be whiter than another, or as that which has the same quality as another is said to be like it. But the other classes of things are a (+) result of relation rather than a (-) cause of it. For the category when consists in a relation to time; and the category where in a relation to place. And posture implies an arrangement of parts; and having (attire), the relation of the thing having to the things had.
lib. 5 l. 17 n. 6 Deinde cum dicit dicuntur autem prosequitur tres modos enumeratos; et primo prosequitur primum. Secundo prosequitur secundum, ibi, activa vero et passiva. Tertio tertium, ibi, ergo secundum numerum. Circa primum duo facit. Primo ponit relationes quae consequuntur numerum absolute. Secundo ponit relationes quae consequuntur unitatem absolute, ibi, et amplius aequale. Dicit ergo, quod primus modus relationum, qui est secundum numerum, distinguitur hoc modo: quia vel est secundum comparationem numeri ad numerum, vel numeri ad unum. Et secundum comparationem ad utrumque dupliciter: quia vel est secundum comparationem numeri indeterminate ad numerum, aut ad unum determinate. Et hoc est quod dicit, quod prima, quae dicuntur ad aliquid secundum numerum, aut dicuntur simpliciter, idest universaliter, vel indeterminate, aut determinate. Et utrolibet modo ad eos, scilicet numeros. Aut ad unum, idest ad unitatem.	1006. The first things (493). Then he proceeds to deal with the three senses of relation which have been enumerated. First, he considers the first sense. Second (1023), he treats the second sense (“Active and passive”). Third (1026), he attends to the third sense (“Therefore, things”). In regard to the first he does two things. First, he describes the relations which are based simply on number; and second (1022), he treats those which are based simply on unity (“Further, equal”). He says, first, that the first way in which things are relative, which is numerical, is divided inasmuch as the relation is based on (a) the ratio of one number to another or (b) on that of a number to unity. And in either case it may be taken in two ways, for the number which is referred to another number or to unity in the ratio on which the relation is based is either definite or indefinite. This is his meaning in saying that the first things which are said to be relative numerically are said to be such “without qualification,” i.e., in general or indefinitely, “or else definitely.” And in both ways “to them,” namely, to numbers, “or to unity,” i.e., to the unit.
lib. 5 l. 17 n. 7 Sciendum est autem, quod omnis mensuratio, quae est in quantitatibus continuis, aliquo modo derivatur a numero. Et ideo relationes, quae sunt secundum quantitatem continuam, etiam attribuuntur numero.	1007. Now it should be borne in mind that every measure which is found in continuous quantities is derived in some way from number. Hence relations which are based on continuous quantity are also attributed to number.
lib. 5 l. 17 n. 8 Sciendum est etiam, quod proportio numeralis dividitur primo in duas; scilicet aequalitatis, et inaequalitatis. Inaequalitatis autem sunt duae species; scilicet excedens et excessum, et magis et minus. Inaequale autem excedens in quinque species dividitur.	1008. It should also be borne in mind that numerical ratios are divided first into two classes, that of equality and that of inequality. And there are two kinds of inequality: the larger and smaller, and more and less. And the larger is divided into five kinds.
lib. 5 l. 17 n. 9 Numerus enim maior quandoque respectu minoris est multiplex; quando scilicet aliquoties continet ipsum, sicut sex continet duo ter. Et si quidem contineat ipsum bis, dicitur duplum; sicut duo ad unum vel quatuor ad duo. Si ter, triplum. Si quater, quadruplum. Et sic inde.	1009. For a number is larger whenever it is multiple with respect to a smaller number, i.e., when it includes it many times, as six includes two three times. And if it includes it twice, it is called double; as two in relation to one, or four to two. And if it includes it three times, it is called triple; and if four times, quadruple; and so on.
lib. 5 l. 17 n. 10 Quandoque vero numerus maior continet totum numerum minorem semel, et insuper unam aliquam partem eius. Et tunc dicitur superparticularis. Et si quidem contineat totum et medium, vocatur sesquialterum, sicut tria ad duo. Si autem tertiam, sesquitertius, sicut quatuor ad tria. Si quartam, sesquiquartus, sicut quinque ad quatuor. Et sic inde.	1010. But sometimes a larger number includes a whole smaller number once and some part of it besides; and then it is said to be superparticular. If it includes a whole smaller number and a half of it besides, it is called sesquialteral, as three to two; and if a third part besides, it is called sesquitertian, as four to three; and if a fourth part besides, it is called sesquiquartan, as five to four; and so on.
lib. 5 l. 17 n. 11 Quandoque numerus maior continet minorem totum semel; et insuper non solum unam partem, sed plures partes. Et sic dicitur superpartiens. Et si quidem contineat duas partes, dicitur superbipartiens, sicut quinque se habent ad tria. Si vero tres, dicitur supertripartiens, sicut septem se habent ad quatuor. Si autem quatuor, sic est superquadripartiens; et sic se habet novem ad quinque. Et sic inde.	1011. Sometimes a larger number includes a whole smaller number once and not merely one part but many parts besides, and then it is called superpartient. And if it includes two parts, it is called superbipartient, as five to three. Again, if it includes three parts, then it is called supertripartient, as seven to four; and if it includes four parts, it is superquadripartient, and then it is related as nine to five; and so on.
lib. 5 l. 17 n. 12 Quandoque vero numerus maior continet totum minorem pluries, et insuper aliquam partem eius; et tunc dicitur multiplex superparticularis. Et si quidem contineat ipsum bis et mediam partem eius, dicitur duplum sesquialterum, sicut quinque ad duo. Si autem ter et mediam partem eius, vocabitur triplum sesquialterum, sicut se habent septem ad duo. Si autem quater et dimidiam partem eius, dicitur quadruplum sesquialterum, sicut novem ad duo. Possent etiam ex parte superparticularis huiusmodi proportionis species sumi, ut dicatur duplex sesquitertius, quando maior numerus habet minorem bis et tertiam partem eius, sicut se habent septem ad tria: vel duplex sesquiquartus, sicut novem ad quatuor, et sic de aliis.	1012. Sometimes a larger number includes a whole smaller number many times and some part of it besides, and then it is called multiple superparticular. If it includes it two and a half times, it is called double sesquialteral, as five to two. If it includes it three and a half times, it is called triple sesquialteral, as seven to two. And if it includes it four and a half times, it is called quadruple sesquialteral, as nine to two. And the species of this kind of ratio can also be considered in the case of the superparticular, inasmuch as we speak of the double sesquitertian ratio when a greater number includes a smaller number two and a third times, as seven to three; or of the double sesquiquartan, as nine to four; and so on.
lib. 5 l. 17 n. 13 Quandoque etiam numerus maior habet minorem totum pluries, et etiam plures partes eius, et tunc dicitur multiplex superpartiens. Et similiter proportio potest dividi secundum species multiplicitatis, et secundum species superpartientis, si dicatur duplum superbipartiens, quando habet maior numerus totum minorem bis et duas partes eius, sicut octo ad tria. Vel etiam triplum superbipartiens, sicut undecim ad tres. Vel etiam duplum supertripartiens, sicut undecim ad quatuor. Habet enim totum bis, et tres partes eius.	1013. Sometimes too a larger number includes a whole smaller number many times and many parts of it besides, and then it is called multiple superpartient. And similarly a ratio can be divided from the viewpoint of the species of multiplicity, and from that of the species of the superpartient, provided that we may speak of a double superbipartient, when a greater number includes a whole smaller number twice and two parts of it, as eight to three; or even of triple superbipartient, as eleven to three; or even of double supertripartient, as eleven to four. For it includes a whole number twice and three parts of it besides.
lib. 5 l. 17 n. 14 Et totidem species sunt ex parte inaequalitatis eius qui exceditur. Nam numerus minor dicitur submultiplex, subparticularis, subpartiens, submultiplex subparticularis, submultiplex subpartiens, et sic de aliis.	1014. And there are just as many species of inequality in the case of a smaller number. For a smaller number is called submultiple, subpartient, submultiple superparticular, submultiple superpartient, and so on.
lib. 5 l. 17 n. 15 Sciendum autem quod prima species proportionis, scilicet multiplicitas, consistit in comparatione unius numeri ad unitatem. Quaelibet enim eius species invenitur primo in aliquo numero respectu unitatis. Duplum primo invenitur in binario respectu unitatis. Et similiter proportio tripli in ternario respectu unitatis, et sic de aliis. Primi autem termini in quibus invenitur aliqua proportio, dant speciem ipsi proportioni. Unde in quibuscumque aliis terminis consequenter inveniatur, invenitur in eis secundum rationem primorum terminorum. Sicut proportio dupla primo invenitur inter duo et unum. Unde ex hoc proportio recipit rationem et nomen. Dicitur enim proportio dupla proportio duorum ad unum. Et propter hoc, si etiam unus numerus respectu alterius numeri sit duplus, tamen hoc est secundum quod minor numerus accipit rationem unius, et maior rationem duorum. Sex enim se habet in dupla proportione ad tria, inquantum tria se habent ad sex ut unum ad duo. Et simile est in tripla proportione, et in omnibus aliis speciebus multiplicitatis. Et ideo dicit, quod ista relatio dupli, est per hoc quod numerus determinatus, scilicet duo, refertur ad unum, idest ad unitatem.	1015. But it must be noted that the first species of ratio, namely, multiplicity, consists in the relation of one number to the unit. For any species of it is found first in the relation of some number to the unit. Double, for example, is found first in the relation of two to the unit. And similarly a triple ratio is found in the relation of three to the unit; and so on in other cases. But the first terms in which any ratio is found give species to the ratio itself. Hence in whatever other terms it is subsequently found, it is found in them according to the ratio of the first terms. For example, the double ratio is found first between two and the unit. It is from this, then, that the ratio receives its meaning and name; for a double ratio means the ratio of two to the unit. And it is for this reason too that we use the term in other cases; for even though one number is said to be double another, this happens only inasmuch as a smaller number takes on the role of the unit and a larger number the role of two; for six is related to three in a double ratio, inasmuch as six is to three as two is to one. And it is similar in the case of a triple ratio, and in all other species of multiplicity. Hence he says that the relation of double is a result of the fact that a definite number, i.e., two, “is referred to unity,” i.e., to the unit.
lib. 5 l. 17 n. 16 Sed hoc quod dico, multiplex, importat relationem numeri ad unitatem; sed non alicuius determinati numeri, sed numeri in universali. Si enim determinatus numerus accipiatur ut binarius vel ternarius, esset una species multiplicitatis, ut dupla vel tripla. Sicut autem duplum se habet ad duo, et triplum ad tria, quae sunt numeri determinati, ita multiplex ad multiplicitatem, quia significat numerum indeterminatum.	1016. But the term multiple implies the relation of a number to the unit, not of any definite number but of number in general. For if a definite number were taken, as two or three, there would be one species of multiplicity, as double or triple. And just as the double is related to two and the triple to three, which are definite numbers, so too the multiple is related to multiplicity, because it signifies an indefinite number.
lib. 5 l. 17 n. 17 Aliae autem proportiones non possunt attendi secundum numerum ad unitatem, scilicet neque proportio superparticularis, neque superpartiens, neque multiplex superparticularis, neque multiplex superpartiens. Omnes enim hae proportionum species attenduntur secundum quod maior numerus continet minorem semel, vel aliquoties; et insuper unam vel plures partes eius. Unitas autem partem habere non potest: et ideo nulla harum proportionum potest attendi secundum comparationem numeri ad unitatem, sed secundum comparationem numeri ad numerum. Et sic est duplex, vel secundum numerum determinatum, vel secundum numerum indeterminatum.	1017. Other ratios, however, cannot be reduced to the relation of a number to the unit: either a superparticular ratio, or a superpartient, or a multiple superparticular, or a multiple superpartient. For all of these species of ratios are based on the fact that a larger number includes a smaller number once, or some part of it, and one or several parts of it besides. But the unit cannot have a part, and therefore none of these ratios can be based on the relation of a number to the unit but on the relation of one number to another. Thus the double ratio is either that of a definite number, or that of an indefinite number.
lib. 5 l. 17 n. 18 Si autem secundum numerum determinatum, sic est hemiolum, idest sesquialterum, aut subhemiolum, idest supersesquialterum. Proportio enim sesquialtera primo consistit in his terminis, scilicet ternario et binario; et sub ratione eorum in omnibus aliis invenitur. Unde quod dicitur hemiolum vel sesquialterum importat relationem determinati numeri ad determinatum numerum, scilicet trium ad duo.	1018. And if it is that of a definite number, then “it is what is one and a half times as great,” i.e., sesquialteral, or “that which it exceeds,” i.e., supersesquialteral. For a sesquialteral ratio consists first in these terms: three and two; and in the ratio of these it is found in all other cases. Hence what is called one and a half times as great, or sesquialteral, implies the relation of one definite number to another, namely, of three to two.
lib. 5 l. 17 n. 19 Quod vero dicitur superparticulare, refertur ad subparticulare, non secundum determinatos numeros, sicut etiam multiplex refertur ad unum, sed secundum numerum indeterminatum. Primae enim species inaequalitatis superius numeratae accipiuntur secundum indeterminatos numeros, ut multiplex, superparticulare, superpartiens et cetera. Species vero istorum accipiuntur secundum numeros determinatos, ut duplum, triplum, sesquialterum, sesquitertium, et sic de aliis.	1019. But the relation which is called superparticular is relative to the subparticular, not according to any definite number, as the multiple is relative also to the unit, but according to an indefinite number. For the first species of inequality given above (1008) are taken according to indefinite numbers, for example, the multiple, superparticular, superpartient, and so on. But the species of these are taken according to definite numbers, as double, triple, sesquialteral, sesquiquartan, and so on.
lib. 5 l. 17 n. 20 Contingit enim aliquas quantitates continuas habere proportionem adinvicem, sed non secundum aliquem numerum, nec determinatum, nec indeterminatum. Omnium enim quantitatum continuarum est aliqua proportio; non tamen est proportio numeralis. Quorumlibet enim duorum numerorum est una mensura communis, scilicet unitas, quae aliquoties sumpta, quemlibet numerum reddit. Non autem quarumlibet quantitatum continuarum invenitur esse una mensura communis; sed sunt quaedam quantitates continuae incommensurabiles: sicut diameter quadrati est incommensurabilis lateri. Et hoc ideo, quia non est proportio eius ad latus, sicut proportio numeri ad numerum, vel numeri ad unum.	1020. Now it happens that some continuous quantities have a ratio to each other which does not involve any number, either definite or indefinite. For there is some ratio between all continuous quantities, although it is not a numerical ratio. For there is one common measure of any two numbers, namely, the unit, which, when taken many times, yields a number. But no common measure of all continuous quantities can be found, since there are certain incommensurable continuous quantities, as the diameter of a square is incommensurable with one of its sides. The reason is that there is no ratio between it and one of its sides like the ratio of one number to another or of a number to the unit.
lib. 5 l. 17 n. 21 Cum ergo dicitur in quantitatibus, quod haec est maior illa, vel se habet ad illam ut continens ad contentum, non solum haec ratio non attenditur secundum aliquam determinatam speciem numeri, sed nec etiam quod sit secundum numerum, quia omnis numerus est alteri commensurabilis. Omnes enim numeri habent unam communem mensuram, scilicet unitatem. Sed continens et contentum non dicuntur secundum aliquam commensurationem numeralem. Continens enim ad contentum dicitur, quod est tantum, et adhuc amplius. Et hoc est indeterminatum, utrum sit commensurabile, vel non commensurabile. Quantitas enim qualiscumque accipiatur, vel est aequalis, vel inaequalis. Unde, si non est aequalis, sequitur quod sit inaequalis et continens, etiam si non sit commensurabilis. Patet igitur quod omnia praedicta dicuntur ad aliquid secundum numerum, et secundum passiones numerorum, quae sunt commensuratio, proportio, et huiusmodi.	1021. Therefore, when it is said in the case of quantities that this quantity is greater than that one, or is related to that one as what includes is related to what is included in it, not only is this ratio not considered according to any definite species of number, but it is not even considered according to number at all, because every number is commensurable with another. For all numbers have one common measure, which is the unit. But what includes and what is included in it are not spoken of according to any numerical measure; for it is what is so much and something more that is said to have the relation of what includes to what is included in it. And this is indefinite, whether it be commensurable or incommensurable; for whatever quantity may be taken, it is either equal or unequal. If it is not equal, then it follows that it is unequal and includes something else, even though it is not commensurable. Hence it is clear that all of the above-mentioned things are said to be relative according to number and to the properties of numbers, which are commensuration, ratio, and the like.
lib. 5 l. 17 n. 22 Deinde cum dicit et amplius ponit relativa, quae accipiuntur secundum unitatem, et non per comparationem numeri ad unum vel ad numerum; et dicit quod alio modo a praedictis dicuntur relative, aequale, simile, et idem. Haec enim dicuntur secundum unitatem. Nam eadem sunt, quorum substantia est una. Similia, quorum qualitas est una. Aequalia, quorum quantitas est una. Cum autem unum sit principium numeri et mensura, patet etiam, quod haec dicuntur ad aliquid secundum numerum, idest secundum aliquid ad genus numeri pertinens; non eodem modo tamen haec ultima cum primis. Nam primae relationes erant secundum numerum ad numerum, vel secundum numerum ad unum; hoc autem secundum unum absolute.	1022. Further, equal (494). He now treats those relative terms which have a reference to unity or oneness and are not based on the relation of one number to another or to the unit. He says that equal, like and same are said to be relative in a different way than the foregoing. For these are called such in reference to unity. For those things are the same whose substance is one; and those are alike whose quality is one; and those are equal whose quantity is one. Now since unity is the principle and measure of number, it is also clear that the former terms are said to be relative “numerically,” i.e., in reference to something belonging to the class of number. But these last terms are not said to be relative in the same way as the first. For the first relations seen are those of number to number, or of a number to the unit; but this relation has to do with unity in an absolute sense.
lib. 5 l. 17 n. 23 Deinde cum dicit activa vero prosequitur de secundo modo relationum, quae sunt in activis et passivis: et dicit, quod huiusmodi relativa sunt relativa dupliciter. Uno modo secundum potentiam activam et passivam; et secundo modo secundum actus harum potentiarum, qui sunt agere et pati; sicut calefactivum dicitur ad calefactibile secundum potentiam activam et passivam. Nam calefactum est, quod potest calefacere; calefactibile vero, quod potest calefieri. Calefaciens autem ad calefactum, et secans ad id quod secatur, dicuntur relative secundum actus praedictarum potentiarum.	1023. Active and passive (495). (2) Here he proceeds to treat the second type of relations, which pertains to active and passive things. He says that relative beings of this kind are relative in two ways: in one way according to active and passive potency; and in a second way according to the actualizations of these potencies, which are action and passivity; for example, what can heat is said to be relative to what can be heated in virtue of active and passive potency. For it is what is capable of heating that can heat, and it is what is capable of being heated that can become hot. Again, what is heating in relation to what is heated, and what is cutting in relation to what is being cut, are said to be relative according to the operations of the aforesaid potencies.
lib. 5 l. 17 n. 24 Et differt iste modus relationum a praemissis. Quae enim sunt secundum numerum, non sunt aliquae actiones nisi secundum similitudinem, sicut multiplicare, dividere et huiusmodi, ut etiam in aliis dictum est, scilicet in secundo physicorum; ubi ostendit, quod mathematica abstrahunt a motu, et ideo in eis esse non possunt huiusmodi actiones, quae secundum motum sunt.	1024. Now this type of relation differs from those previously given; for those which are numerical are operations only figuratively, for example, to multiply, to divide, and so forth, as has also been stated elsewhere, namely, in Book II of the Physics, where he shows that the objects of mathematics abstract from motion, and therefore they cannot have operations of the kind that have to do with motion.
lib. 5 l. 17 n. 25 Sciendum etiam est quod eorum relativorum, quae dicuntur secundum potentiam activam et passivam, attenditur diversitas secundum diversa tempora. Quaedam enim horum dicuntur relative secundum tempus praeteritum, sicut quod fecit, ad illud quod factum est; ut pater ad filium, quia ille genuerit, iste genitus est; quae differunt secundum fecisse, et passum esse. Quaedam vero secundum tempus futurum, sicut facturus refertur ad faciendum. Et ad hoc genus relationum reducuntur illae relationes, quae dicuntur secundum privationem potentiae, ut impossibile et invisibile. Dicitur enim aliquid impossibile huic vel illi; et similiter invisibile.	1025. It should also be noted that among relative terms based on active and passive potency we find diversity from the viewpoint of time; for some of these terms are predicated relatively with regard to past time, as what has made something to what has been made; for instance, a father in relation to his son, because the former has begot and the latter has been begotten; and these differ as what has acted and what has been acted upon. And some are used with respect to future time, as when what will make is related to what will be made. And those relations which are based on privation of potency, as the impossible and the invisible, are reduced to this class of relations. For something is said to be impossible for this person or for that one; and the invisible is spoken of in the same way.
lib. 5 l. 17 n. 26 Deinde cum dicit ergo secundum prosequitur de tertio modo relationum; et dicit quod in hoc differt iste tertius modus a praemissis, quod in praemissis, unumquodque dicitur relative ex hoc, quod ipsum ad aliud refertur; non ex eo quod aliud referatur ad ipsum. Duplum enim refertur ad dimidium, et e converso; et similiter pater ad filium, et e converso; sed hoc tertio modo aliquid dicitur relative ex eo solum, quod aliquid refertur ad ipsum; sicut patet, quod sensibile et scibile vel intelligibile dicuntur relative, quia alia referuntur ad illa. Scibile enim dicitur aliquid, propter hoc, quod habetur scientia de ipso. Et similiter sensibile dicitur aliquid quod potest sentiri.	1026. Therefore, things (496). (3) Next he proceeds to deal with the third type of relations. He says that this third type differs from the foregoing in this way, that each of the foregoing things is said to be relative because each is referred to something else, not because something else is referred to it. For double is related to half, and vice versa; and in a similar way a father is related to his son, and vice versa. But something is said to be relative in this third way because something is referred to it. It is clear, for example, that the sensible and the knowable or intelligible are said to be relative because other things are related to them; for a thing is said to be knowable because knowledge is had of it. And similarly something is said to be sensible because it can be sensed.
lib. 5 l. 17 n. 27 Unde non dicitur relative propter aliquid quod sit ex eorum parte, quod sit qualitas, vel quantitas, vel actio, vel passio, sicut in praemissis relationibus accidebat; sed solum propter actiones aliorum, quae tamen in ipsa non terminantur. Si enim videre esset actio videntis perveniens ad rem visam, sicut calefactio pervenit ad calefactibile; sicut calefactibile refertur ad calefaciens, ita visibile referretur ad videntem. Sed videre et intelligere et huiusmodi actiones, ut in nono huius dicetur, manent in agentibus, et non transeunt in res passas; unde visibile et scibile non patitur aliquid, ex hoc quod intelligitur vel videtur. Et propter hoc non ipsamet referuntur ad alia, sed alia ad ipsa. Et simile est in omnibus aliis, in quibus relative aliquid dicitur propter relationem alterius ad ipsum, sicut dextrum et sinistrum in columna. Cum enim dextrum et sinistrum designent principia motuum in rebus animatis, columnae et alicui inanimato attribui non possunt, nisi secundum quod animata aliquo modo se habeant ad ipsam, sicut columna dicitur dextra, quia homo est ei sinister. Et simile est de imagine respectu exemplaris, et denario, quo fit pretium emptionis. In omnibus autem his tota ratio referendi in duobus extremis, pendet ex altero. Et ideo omnia huiusmodi quodammodo se habent ut mensurabile et mensura. Nam ab eo quaelibet res mensuratur, a quo ipsa dependet.	1027. Hence they are not said to be relative because of something which pertains to them, such as quality, quantity, action, or undergoing, as was the case in the foregoing relations, but only because of the action of other things, although these are not terminated in them. For if seeing were the action of the one seeing as extending to the thing seen, as heating extends to the thing which can be heated, then just as what can be heated is related to the one heating, so would what is visible be related to the one seeing. But to see and to understand and actions of this kind, as is stated in Book IX (1788) of this work, remain in the things acting and do not pass over into those which are acted upon. Hence what is visible or what is knowable is not acted upon by being known or seen. And on this account these are not referred to other things but others to them. The same is true in all other cases in which something is said to be relative because something else is related to it, as right and left in the case of a pillar. For since right and left designate starting points of motion in living things, they cannot be attributed to a pillar or to any nonliving thing except insofar as living things are related to a pillar in some way. It is in this sense that one speaks of a right-hand pillar because a man stands to the left of it. The same holds true of an image in relation to the original; and of a denarius, by means of which one fixes the price of a sale. And in all these cases the whole basis of relation between two extremes depends on something else. Hence all things of this kind are related in somewhat the same way as what is measurable and its measure. For everything is measured by the thing on which it depends.
lib. 5 l. 17 n. 28 Sciendum est autem, quod quamvis scientia secundum nomen videatur referri ad scientem et ad scibile, dicitur enim scientia scientis, et scientia scibilis, et intellectus ad intelligentem et intelligibile; tamen intellectus secundum quod ad aliquid dicitur, non ad hoc cuius est sicut subiecti dicitur: sequeretur enim quod idem relativum bis diceretur. Constat enim quoniam intellectus dicitur ad intelligibile, sicut ad obiectum. Si autem diceretur ad intelligentem, bis diceretur ad aliquid; et cum esse relativi sit ad aliud quodammodo se habere, sequeretur quod idem haberet duplex esse. Et similiter de visu patet quod non dicitur ad videntem, sed ad obiectum quod est color vel aliquid aliud tale. Quod dicit propter ea, quae videntur in nocte non per proprium colorem, ut habetur in secundo de anima.	1028. Now it must be borne in mind that, even though verbally knowledge would seem to be relative to the knower and to the object of knowledge (for we speak both of the knowledge of the knower and of the knowledge of the thing known), and thought to the thinker and to what is thought, nevertheless a thought as predicated relatively is not relative to the one whose thought it is as its subject, for it would follow that the same relative term would then be expressed twice. For it is evident that a thought is relative to what is thought about as to its object. Again, if it were relative to the thinker, it would then be called relative twice; and since the very existence of what is relative is to be relative in some way to something else, it would follow that the same thing would have two acts of existence. Similarly in the case of sight it is clear that sight is not relative to the seer but to its object, which is color, “or something of this sort.” He says this because of the things which are seen at night but not by means of their proper color, as is stated in The Soul, Book II.
lib. 5 l. 17 n. 29 Quamvis et hoc recte posset dici, scilicet quod visus sit videntis. Refertur autem visus ad videntem, non inquantum est visus, sed inquantum est accidens, vel potentia videntis. Relatio enim respicit aliquid extra, non autem subiectum nisi inquantum est accidens. Et sic patet, quod isti sunt modi, quibus aliqua dicuntur secundum se ad aliquid.	1029. And although it is correct to say that sight is of him who sees, sight is not related to the seer formally as sight but as an accident or power of the seer. For a relation has to do with something external, but a subject does not, except insofar as it is an accident. It is clear, then, that these are the ways in which some things are said to be relative directly.
lib. 5 l. 17 n. 30 Deinde cum dicit illa vero ponit tres modos, quibus aliqua dicuntur ad aliquid non secundum se, sed secundum aliud. Quorum primus est, quando aliqua dicuntur ad aliquid propter hoc quod sua genera sunt ad aliquid, sicut medicina dicitur ad aliquid, quia scientia est ad aliquid. Dicitur enim, quod medicina est scientia sani et aegri. Et isto modo refertur scientia per hoc quod est accidens.	1030. And other things (497). He now gives three ways in which some things are said to be relative not directly but indirectly. The first of these is that in which things are said to be relative because their genera are relative as medicine is said to be relative because science is relative. For medicine is called the science of health and sickness. And science is relative in this way because it is an accident.
lib. 5 l. 17 n. 31 Secundus modus est, quando aliqua abstracta dicuntur ad aliquid, quia concreta habentia illa abstracta ad aliud dicuntur; sicut aequalitas et similitudo dicuntur ad aliquid, quia simile et aequale ad aliquid sunt. Aequalitas autem et similitudo secundum nomen non dicuntur ad aliquid.	1031. The second way is that in which certain abstract terms are said to be relative because the concrete things to which these abstract terms apply are relative to something else. For example, equality and likeness are said to be relative because the like and the equal are relative. But equality and likeness are not considered relative as words.
lib. 5 l. 17 n. 32 Tertius modus est, quando subiectum dicitur ad aliquid, ratione accidentis; sicut homo vel album dicitur ad aliquid, quia utrique accidit duplum esse; et hoc modo caput dicitur ad aliquid, eo quod est pars.	1032. The third way is that in which a subject is said to be relative because of an accident. For example, a man or some white thing is said to be relative because each happens to be double; and in this way a head is said to be relative because it is a part.