Authors/Thomas Aquinas/metaphysics/liber10/lect2

Lecture 2

Latin	English
lib. 10 l. 2 n. 1 Postquam ostendit philosophus quot modis unum dicitur, et quae sit ratio unius, ad quam omnes modi reducuntur, scilicet esse indivisibile; hic ex hac ratione unius ostendit quamdam eius proprietatem, scilicet esse mensuram: et dividitur in partes duas. In prima ostendit, quomodo uni competit ratio mensurae, et aliis generibus accidentium. In secunda vero ostendit quomodo unum habens rationem mensurae inveniatur in substantia, ibi, secundum substantiam vero et naturam. Circa primum duo facit. Primo ostendit in quo genere primo inveniatur unum habens rationem mensurae; et quomodo exinde ad alia derivetur secundum propriam rationem mensurae. Secundo ponit quomodo derivetur ad alia secundum quamdam similitudinem, ibi, et scientiam autem rerum metrum. Circa primum duo facit. Primo ostendit ubi primo sit unum rationem mensurae habens, et quomodo exinde ad alia fiat derivatio. Secundo ponit quaedam consideranda circa mensuras, ibi, non semper autem numero unum. Circa primum tria facit. Primo ostendit quomodo unum quod est mensura inveniatur in quantitate, et exinde ad alia genera derivetur. Secundo in qua specie quantitatis est primo, ibi, et quo primo cognoscitur. Tertio quomodo derivetur in alias species quantitatis, ibi, hinc autem et in aliis.	1937. Having explained the various senses in which unity is predicated of things, and having stated what its essential note is, to which all its usages are reduced, i.e., being indivisible, here the Philosopher infers a property of unity from its essential note, namely, that it is a measure. This is divided into two parts. In the first he shows how the notion of a measure belongs to unity and to the various classes of accidents. In the second (1961) he shows how unity in the sense of a measure is found in substances (“It is necessary”). In regard to the first part of this division he does two things. First, he indicates the class of things in which unity in the sense of a measure is primarily found, and how it is transferred from this class to the others with the proper notion of a measure. Second (1956), he explains how it is transferred figuratively to the other classes (“And for the same reason”). In treating the first part he does two things. First, he indicates the class of things in which unity in the sense of a measure is first found, and how it is transferred from this class to the others. Second (1950), he makes a study of measures (“However, a measure”). In regard to the first he does three things. First, he shows how unity as a measure is found in quantity, and how it is transferred from this category to the others. Second (1939), he indicates the species of quantity in which it is first found (“And that by which”). Third (1940), he shows how it is transferred to other species of quantity (“And the measure”).
lib. 10 l. 2 n. 2 Dicit ergo primo, quod cum ratio unius sit indivisibile esse; id autem quod est aliquo modo indivisibile in quolibet genere sit mensura; maxime dicetur in hoc quod est esse primam mensuram cuiuslibet generis. Et hoc maxime proprie dicitur in quantitate, et inde derivatur ad alia genera ratio mensurae. Mensura autem nihil aliud est quam id quo quantitas rei cognoscitur. Quantitas vero rei cognoscitur per unum aut numerum. Per unum quidem, sicut cum dicimus, unum stadium, vel unum pedem. Per numerum autem, sicut dicimus tria stadia, vel tres pedes. Ulterius autem omnis numerus cognoscitur per unum, eo quod unitas aliquoties sumpta quemlibet numerum reddit. Unde relinquitur quod omnis quantitas cognoscatur per unum. Addit autem inquantum quantitas, ut hoc referatur ad mensuram quantitatis. Nam proprietates et alia accidentia quantitatis alio modo cognoscuntur.	1938. He accordingly says, first, that, since the essential note of unity consists in being indivisible, and what is indivisible in each genus is somehow the measure of that genus, unity must be said to be in the highest degree the first measure of each genus. This is said to apply most properly to quantity, and it is from this class that the notion of a measure is transferred to other classes of things. Now a measure is nothing else than that by which a thing’s quantity is known, and this is known by the unit or by a number: by a unit, as when we say one furlong or one foot; and by a number, as when we say three furlongs or three feet. Again, every number is known by the unit because the unit taken a certain number of times gives a number. It follows, then, that every quantity is known by unity. To “quantity” he adds “as quantity,” intending that this be referred to the measure of quantity; for the properties and other accidents of quantity are known in a different way.
lib. 10 l. 2 n. 3 Deinde cum dicit et quo primo dicit in qua specie quantitatis primo sit unum et mensura. Et circa hoc duo facit. Primo ostendit quod ratio mensurae primo invenitur in discreta quantitate, quae est numerus; dicens, quod id quo primo cognoscitur quantitas est ipsum unum, idest unitas, quae est principium numeri. Nam unum in aliis speciebus quantitatis non est ipsum unum, sed aliquid cui accidit unum; sicut dicimus unam manum, aut unam magnitudinem. Unde sequitur, quod ipsum unum, quod est prima mensura, sit principium numeri secundum quod est numerus.	1939. And that by which (821). Then he indicates in what species of quantity unity or measure is primarily found. First, he makes it clear that the notion of a measure is primarily found in discrete quantity, which is number. He says that that by which quantity is first known is “unity itself,” i.e., the unit which is the principle of number. For in other species of quantity the unit is not unity itself but something of which unity is an attribute, as when we speak of one hand or of one continuous quantity. Hence it follows that unity itself, which is the first measure, is the principle of number as number.
lib. 10 l. 2 n. 4 Secundo cum dicit hinc autem ostendit quomodo derivetur in alias species quantitatis. Et circa hoc duo facit. Primo ostendit ad quas species quantitatis derivetur; dicens, quod hinc, scilicet ex numero et uno quod est principium numeri, dicitur mensura in aliis quantitatibus, id scilicet quo primo cognoscitur unumquodque eorum. Et id quod est mensura cuiuslibet generis quantitatis, dicitur unum in illo genere.	1940. And the measure (822). Second, he shows how unity is transferred to other species of quantity; and in regard to this he does two things. First, he indicates the species of quantity to which it is transferred. He says that it is from this class, i.e., from number and from the unit, which is the principle of number, that the notion of a measure is transferred to other quantities as that by which each of them is first known. And whatever is the measure in each class of things is the unit in that class.
lib. 10 l. 2 n. 5 Et hoc exemplificat in tribus generibus; scilicet in dimensionibus quae sunt scilicet longitudo, et latitudo, et profunditas. Et in ponderibus, in hoc quod dicit, in gravitate. Et in motibus, in hoc, quod dicit, in velocitate, quod referatur ad mensuram temporis. Et de dimensionibus quidem nulli dubium erat, quin quantitates essent, et quod proprie eis primo competeret mensurari. Sed de gravitate et velocitate poterat esse dubium, eo quod magis videntur esse qualitates quam quantitates.	1941. He gives examples of this in three classes of things, i.e., in dimensions—length, breadth and width; in weight, or in what he calls heaviness; and in speed, or in what he calls rapidity, which refers to the measure of time. In the case of dimensions no one doubted that they were quantities and that they were properly susceptible to measurement, but in the case of weight and of speed there could be a difficulty because these seem to be qualities rather than quantities.
lib. 10 l. 2 n. 6 Et ideo dicit, quomodo pertinent ad genus quantitatis, et quomodo competit eis mensurari; dicens, quod gravitas et velocitas habent aliquid commune in contrariis, quia scilicet in uno contrariorum invenitur alterum: nam grave est aliquo modo leve, et e converso; et velox est aliquo modo tardum. Utrumque enim eorum est duplex. Sicut grave, uno modo dicitur absolute, scilicet quod habet inclinationem ut feratur ad medium, sine hoc quod consideretur quantum habeat de tali inclinatione: et sic non pertinet ad genus quantitatis, nec competit ei mensurari. Alio modo dicitur grave per comparationem ad aliud, scilicet quod excedit alterum in inclinatione praedicta; ut scilicet dicamus, quod terra est gravis in comparatione ad aquam, et plumbum in comparatione ad lignum. Sic igitur ratione huius excessus, invenitur aliqua ratio quantitatis et mensurae. Et similiter velox dicitur dupliciter. Uno modo absolute, scilicet quod habet motum quemcumque. Et alio modo quod habet excessum motus. Et uno modo competit sibi ratio quantitatis et mensurae. Alio modo non.	1942. He therefore explains how these pertain to the genus of quantity, and how they are susceptible to measurement. He says that heaviness and rapidity have something in common with their contraries because one contrary is found in the other; for what is heavy is in some sense light, and the reverse; and what is rapid is in some sense slow. For each of these terms is used in two senses. (1) In one sense the term heavy is used without qualification of anything that has an inclination to be borne towards the center of the earth, without taking into consideration how great its inclination is; and in this sense heavy does not refer to the category of quantity, and it is not susceptible to measurement. (2) In the other sense it is used of one thing in comparison with something else, namely, of what exceeds something else in terms of the abovementioned inclination; for example, we say that earth is heavy in comparison with water, and that lead is heavy in comparison with wood. Therefore it is by reason of this excess that some notion of quantity and measure is found. The term rapid is similarly used in two senses. In one sense it is used without qualification of anything that has any motion; and in a second sense it is used of anything that has an excessive motion. And in one respect the notions of quantity and measure properly apply to it, and in another respect they do not.
lib. 10 l. 2 n. 7 Et ut exponat quod dixerat de conditione gravitatis et velocitatis in contrariis, subdit quod in ipso tardo invenitur velocitas, inquantum id quod est simpliciter et absolute tardum, per excessum se habet ad tardiora. Et similiter gravitas invenitur in levi, sicut aer est levis ad terram, et gravis ad ignem comparatus.	1943. With a view to clarifying his statement about the condition of heaviness and rapidity in reference to contraries he adds that rapidity is found in something that is slow inasmuch as what is simply and unqualifiedly slow is more rapid in comparison with something that is slower than itself. And in a similar way heaviness is found in light things; for example, air is light in comparison with earth, and heavy in comparison with fire.
lib. 10 l. 2 n. 8 Deinde cum dicit in omnibus ostendit qualiter a numero derivetur ratio mensurae ad alia. Et primo hoc manifestat simul in dimensionibus et ponderibus. Secundo in velocitate motuum, ibi, et motum simplici motu. Dicit ergo primo, quod hoc modo derivatur ratio mensurae a numero ad alias quantitates, quod sicut unum quod est mensura numeri est indivisibile, ita in omnibus aliis generibus quantitatis aliquod unum indivisibile est mensura et principium. Sicut in mensuratione linearum utuntur homines quasi indivisibili, mensura pedali, idest unius pedis: ubique enim quaeritur pro mensura aliquid indivisibile, quod est aliquod simplex, vel secundum qualitatem, vel secundum quantitatem. Secundum qualitatem quidem, ut album in coloribus, quod quodammodo est mensura colorum, ut dicetur infra. Secundum quantitatem vero, ut unitas in numero, et mensura pedalis in lineis.	1944. And in all cases (823). Then he shows how the notion of a measure is transferred from number to other kinds of quantity. He immediately makes this clear, first, in the case of dimensions and in that of weights; and second (1947), in that of the rapidity of motions (“And they also measure”). He accordingly says, first, that the notion of a measure is transferred from number to the other kinds of quantity in this way that, just as the unit which is the measure of number is indivisible, so too all the other kinds of quantity have something that is one and indivisible as their measure and principle. For example, in measuring lines men use “the foot measure,” i.e., the measure of one foot, as something indivisible; for wherever something indivisible is sought as. a measure, there is something simple either in quality or in quantity; in quality, as whiteness in the case of colors, which is in a sense the measure of colors, as will be mentioned below (1968); and in quantity, as the unit in the case of numbers, and the foot measure in the case of lines.
lib. 10 l. 2 n. 9 Assignat autem rationem, quare mensuram oportet esse aliquid indivisibile; quia scilicet hoc est certa mensura, a qua non potest aliquid auferri vel addi. Et ideo unum est mensura certissima; quia unum quod est principium numeri, est omnino indivisibile, nullamque additionem aut subtractionem suscipiens manet unum. Sed mensurae aliorum generum quantitatis imitantur hoc unum, quod est indivisibile, accipiens aliquid minimum pro mensura secundum quod possibile est. Quia si acciperetur aliquid magnum, utpote stadium in longitudinibus, et talentum in ponderibus, lateret, si aliquod modicum subtraheretur vel adderetur; et semper in maiori mensura hoc magis lateret quam in minori.	1945. Further, he points out why a measure must be something indivisible. The reason is that an exact measure must be something which can be neither added to nor subtracted from. Thus the unit is the most exact or certain measure, because the unit which is the principle of number is altogether indivisible, and whatever unity is not susceptible either to addition or to subtraction remains one. The measures of the other classes of quantity resemble this unit which is indivisible inasmuch as men take some smallest thing as a measure to the extent that this is possible. For if anything large were taken, as the furlong among distances and the talent among weights, it would escape our notice if some small portion were subtracted from or added to it. And this would always be more true of a larger measure than of a smaller one.
lib. 10 l. 2 n. 10 Et ideo omnes accipiunt hoc pro mensura tam in humidis, ut est oleum et vinum, quam in siccis, ut est granum et hordeum, quam in ponderibus et dimensionibus, quae significantur per grave et magnitudinem; quod primo invenitur tale, ut ab eo non possit aliquid auferri sensibile vel addi quod lateat. Et tunc putant se cognoscere quantitatem rei certitudinaliter, quando cognoscunt per huiusmodi mensuram minimam.	1946. Hence all men take this as a measure both in the case of liquids, such as oil and wine, and in that of solids, such as grain and barley; and also in that of weights and dimensions, which are designated as heaviness and continuous quantity. And this is first found to be such that nothing perceptible can be subtracted from it or added to it that might escape our notice. And men think they know the quantity of a thing exactly when they know it by the smallest measure of this kind.
lib. 10 l. 2 n. 11 Deinde cum dicit et motum manifestat idem in velocitate motuum; dicens, quod etiam motum mensurant homines motu simplici, idest uniformi et velocissimo quod habet minimum de tempore. Et ideo in astrologia accipiunt tale principium ad mensurandum. Accipiunt enim motum primi caeli, scilicet motum diurnum, qui est regularis et velocissimus, ad quem iudicant et mensurant omnes alios motus.	1947. And they also (824). Then he makes the same thing clear with regard to the rapidity of motions. He says that men also measure motion “by that motion which is simple,” i.e., the motion which is uniform and quickest, because it takes the least time. Hence in astronomy they take such motion as the basis of measurement; for they take the motion of “the first heaven,” i.e., the daily motion, which is regular and quickest, and they judge and measure all other motions by this.
lib. 10 l. 2 n. 12 Et quia ex velocitate et tarditate motuum contingit gravitas et acuitas in sonis, ut determinatur in musica, subdit exemplum de mensuratione sonorum; dicens, quod in musica prima mensura diesis est, idest differentia duorum semitonorum. Tonus enim dividitur in duo semitona inaequalia, ut in musica probatur. Et similiter in voce, mensura est elementum, quia etiam brevitas et longitudo vocis velocitatem et tarditatem motus consequitur.	1948. And because the low and high pitch of sounds results from the quickness and slowness of motions, as is established in the science of music, he adds as an example the measurement of sounds. He says that in music the first measure is the “diesis,” i.e., the difference between two half tones; for a tone is divided into two unequal half tones, as is proved in the science of music. And similarly in speech the measure is the letter, because the shortness or length of a word is a natural consequence of the quickness or slowness of a motion.
lib. 10 l. 2 n. 13 Omnes autem istae mensurae sunt aliquid unum: non ita quod aliqua mensura sit communis omnibus; sed quia quaelibet mensura in se est aliquid unum, ut dictum est.	1949. Now all these something one, not in measures are the sense that some measure is common to all, but in the sense that any measure in itself is something one, as has been pointed out.
lib. 10 l. 2 n. 14 Deinde cum dicit non semper postquam ostendit philosophus ubi sit primo unum habens rationem mensurae, hic determinat quaedam circa mensuras consideranda. Et est primum, quod licet id quod est mensura habeat rationem unius, inquantum accedit ad indivisibilitatem, non tamen necessarium est unum numero esse quod mensurat. Sed aliquando plura sunt mensurantia, sicut in melodiis sunt duae dieses, idest duo semitona. Sed propter parvitatem non discernitur secundum auditum. Nam sensus non percipit differentiam valde parvorum, sed eorum differentia percipitur in rationibus, idest secundum diversas rationes proportionum, quia ex diversis proportionibus numeralibus causantur.	1950. However, a measure (825). After having shown in what class of things unity as a measure is primarily found, here the Philosopher clears up certain points that have to be investigated about measures. The first of these is that, although a measure is understood to be one thing inasmuch as it comes close to being indivisible, it is not necessary that a measure be something numerically one; but sometimes many things are measures; for example, in the case of musical sounds “there are two dieses,” i.e., two half tones. However, because of their smallness they are not distinguished by the sense of hearing, for the senses do not perceive the difference between two things that are very small; but their difference is perceived “in their ratios,” i.e., in the different ratios which comprise their proportions, because they are caused by different numerical proportions.
lib. 10 l. 2 n. 15 Similiter etiam voces quibus etiam mensuramus, plures sunt. Quantitas enim unius metri vel unius pedis, mensuratur ex diversis syllabis, quarum aliae sunt breves, et aliae longae. Similiter etiam est diameter circuli vel quadrati, et etiam latus quadrati: et quaelibet magnitudo mensuratur duobus: non enim invenitur quantitas ignota nisi per duas quantitates notas.	1951. Similarly the things by which we measure words are also many; for the quantity of one meter or of one foot is measured by different syllables, some of which are short and some long. The same thing is true of the diameter of a circle and of the diagonal of a square, and also of the side of a square. And any continuous quantity is measured by two things, for an unknown quantity is found only by means of two known quantities.
lib. 10 l. 2 n. 16 Hoc autem dicto, concludit epilogando quae supra dicta sunt, scilicet quod unum est mensura omnium. Cuius ratio est, quia unum est ad quod terminatur divisio. Ea vero, ex quibus est substantia uniuscuiusque, cognoscuntur per divisionem sive resolutionem totius in componentia; sive sint partes secundum quantitatem, sive sint partes secundum speciem, ut materia et forma, et elementa corporum mixtorum. Et ideo oportet id quod est per se unum, esse indivisibile, cum sit mensura qua cognoscitur res; quia quod in singulis est primum in compositione et ultimum in resolutione, est indivisibile, et per hoc cognoscitur res, ut dictum est.	1952. Having said this he brings this part of his discussion to a close by summarizing what has been said above, namely, that unity constitutes the measure of all things. The reason for this is that unity is the term of division. And those principles which constitute the substance of each thing are known by the division or dissolution of the whole into its component parts, whether they are quantitative parts or specific parts such as matter and form and the elements of compounds. Therefore what is one in itself must be indivisible since it is the measure by which a thing is known, because in the case of singular things whatever is first in the process of composition and last in the process of dissolution is indivisible, and it is by means of this that the thing is known, as has been explained.
lib. 10 l. 2 n. 17 Sed tamen non similiter in omnibus invenitur indivisibile; sed quaedam sunt omnino indivisibilia, sicut unitas quae est principium numeri. Quaedam vero non sunt omnino indivisibilia, sed indivisibilia secundum sensum, secundum quod voluit auctoritas instituentium tale aliquid pro mensura; sicut mensura pedalis, quae quidem indivisibilis est proportione, sed non natura. Nam omne continuum forsan divisibile est. Dicit autem forsan propter dubitationem quorumdam ponentium magnitudinem componi ex indivisibilibus; vel quia magnitudines naturales non dividuntur in infinitum, sed solae mathematicae. Est enim invenire minimam carnem, ut tangitur primo physicorum.	1953. Yet indivisibility is not found in all things in the same way. (1) Some things are altogether indivisible, such as the unit which is the basis of number, whereas (2) others are not altogether indivisible but only to the senses, according as the authority of those who instituted such a measure wished to consider something as a measure; for example, the foot measure, which is indivisible in proportion [to the things measured] but not by nature. “For perhaps everything continuous is divisible”; and he says “perhaps” because of the difficulty facing those men who claimed that continuous quantity is composed of indivisible elements, or that natural continuous quantities are not infinitely divisible, but only mathematical quantities. For it is possible to find the smallest amount of flesh, as is mentioned in Book I of the Physics.
lib. 10 l. 2 n. 18 Deinde cum dicit semper autem ponit secundum quod considerandum est circa mensuram; dicens, quod metrum, idest mensura, semper debet esse cognatum, scilicet eiusdem naturae vel mensurae, cum mensurato: sicut mensura magnitudinum debet esse magnitudo: et non sufficit quod conveniat in natura communi, sicut omnes magnitudines conveniunt: sed oportet esse convenientiam mensurae ad mensuratum in natura speciali secundum unumquodque, sic quod longitudinis sit longitudo mensura, latitudinis latitudo, vox vocis, et gravitas gravitatis, et unitatum unitas.	1954. And a measure (826). Then he gives the second point that has to be investigated about a measure. He says that “the meter,” i.e., the measure, should always be of the same kind as the thing measured, i.e., of the same nature or measure as the thing measured; for example, a continuous quantity should be the measure of continuous quantities; and it is not enough that they have a common nature, as all continuous quantities do, but there must be some agreement between the measure and the thing measured in the line of their special nature. Thus a length is the measure of lengths, a width of widths, a vocal sound of vocal sounds, a weight of weights, and a unit of units.
lib. 10 l. 2 n. 19 Sic enim oportet accipere ut absque calumnia loquamur; sed non quod numerorum mensura sit numerus. Numerus autem non habet rationem mensurae primae, sed unitas. Et si unitas mensura est, ad significandum convenientiam inter mensuram et mensuratum, oportet dicere, quod unitas sit mensura unitatum, et non numerorum. Et tamen si rei veritas attendatur, oportebit hoc etiam concedere, quod numerus esset mensura numerorum, aut etiam unitas numerorum similiter acciperetur. Sed non similiter dignum videtur dicere unitatem esse mensuram unitatum, et numerum numeri, vel unitatem numeri; propter differentiam, quae videtur esse inter unitatem et numerum. Sed istam differentiam observare, idem est, ac si quis dignum diceret quod unitates essent mensurae unitatum, sed non unitas; quia unitas differt ab unitatibus ut singulariter prolatum ab his quae pluraliter proferuntur. Et similis ratio est de numero ad unitatem; quia numerus nihil aliud est quam pluralitas unitatum. Unde nihil aliud est dicere unitatem esse mensuram numeri, quam unitatem esse mensuram unitatum.	1955. “For this is the view which must be taken” in order that we may speak without being criticized, “but not that number is the measure of numbers.” Now number does not have the notion of a first measure but unity does; and if unity is a measure, then in order to signify the agreement between the measure and the thing measured it will be necessary to say that unity is the measure of units and not of numbers. Yet if the truth of the matter be taken into consideration, it will be necessary to admit also that number is the measure of numbers or even that the unit may be taken in a similar way as the measure of numbers. But it does not seem equally fitting to say that the unit is the measure of units and number of number or unity of number, because of the difference which appears to exist between the unit and number. But to observe this difference is the same as if someone were to say that it is fitting for units to be the measure of units but not the unit, because the unit differs from units as things expressed in the singular differ from those expressed in the plural. And the same argument applies to number in relation to the unit, because a number is nothing else than a plurality of units. Hence to say that the unit is the measure of number is merely to say that the unit is the measure of units.
lib. 10 l. 2 n. 20 Deinde cum dicit et scientiam ostendit qualiter mensura transfertur ad quaedam secundum similitudinem; dicens, quod cum dictum sit quod mensura est, qua quantitas rei cognoscitur, dicemus scientiam esse mensuram rerum scibilium et sensum rerum sensibilium, quia ipsis aliquid cognoscimus, sensu scilicet sensibilia et scientia scibilia. Non tamen eodem modo sicut mensura. Nam per mensuram cognoscitur aliquid sicut per principium cognoscendi: per sensum autem et scientiam sicut per potentiam cognoscitivam, aut habitum cognoscitivum.	1956. And for the same reason (827). Then he shows how the term measure is transferred in a figurative way to another class of things. He says that, since it has been stated that a measure is that by which the quantity of a thing is known, we may say that intellectual knowledge is the measure of that which is knowable intellectually, and that sensory perception is the measure of that which is perceptible; because we know something by means of them, namely, sensible objects by means of perception and intelligible objects by means of intellectual knowledge; but we do not know them in the same was as we do by a measure. For something is known by a measure as a principle of knowledge, whereas in sensation and knowledge we are measured by things that are outside ourselves.
lib. 10 l. 2 n. 21 Sic igitur per hanc similitudinem dicuntur mensurae, quia secundum rei veritatem magis mensurantur quam mensurent. Non enim quia nos aliquid sentimus aut scimus, ideo sic est in rerum natura. Sed quia sic est in rerum natura, ideo vero aliquid scimus, aut sentimus, ut dicitur nono metaphysicorum. Et sic accidit nobis, quod in sentiendo et sciendo mensuramur per res quae extra nos sunt.	1957. Therefore they are called measures figuratively, because in reality they are measured rather than measure. For it is not because we perceive or know a thing that it is so in reality; but it is because it is so in reality that we have a true knowledge or perception of it, as is said in Book IX (807:C 1896). Thus it follows that in perceiving and knowing something we measure our knowledge by means of the things which exist outside the mind.
lib. 10 l. 2 n. 22 Nobis autem cognoscentibus et mensurantibus, sicut aliquo alio nos mensurante, cognoscimus quanti sumus in quantitate corporali per mensuram cubitalem applicatam nobis. Et sic sicut cubitus exterius appositus est mensura quantitatis corporalis nostrae, ita res scitae vel per sensum apprehensae, sunt mensurae per quas potest sciri utrum vere cognoscamus aliquid per sensum vel per intellectum.	1958. However, in knowing and measuring ourselves by some other measure we know how much bodily quantity we have by applying the cubit measure to ourselves. Hence, just as the external cubit is offered as a measure of our bodily quantity, in a similar way the things known or sensuously apprehended are the measures whereby we can know whether we truly apprehend something by our senses or by our intellect.
lib. 10 l. 2 n. 23 Si qua vero scientia est quae est causa rei scitae, oportebit quod sit eius mensura. Ut scientia artificis est mensura artificiatorum; quia unumquodque artificiatum secundum hoc perfectum est, quod attingit ad similitudinem artis. Et hoc modo se habet scientia Dei respectu omnium. Sed Protagoras dixit hominem esse mensuram omnium rerum inquantum est sciens aut sentiens, quia scientia et sensus sunt mensura substantiarum, scilicet sensibilium et scibilium. Dicebant enim Protagorici, ut in quarto habitum est, quod res sunt tales, quia sic sentimus eas, vel sic opinamur in eis. Cum igitur nihil superabundans vel magnum dicant, videntur tamen aliquid dicere, quia occulte insinuant quae dicere volunt.	1959. And if there is a science which is the cause of the. thing known, it must be this science which measures that thing, just as the science of the master planner is the measure of things made by art, because anything made by art is complete insofar as it attains a likeness to the art. It is in this way that the science of God is related to all things. But Protagoras said that man is the measure of all things inasmuch as he knows or perceives them, because knowledge and perception are the measure of substances, i.e., of things which are intelligible and perceptible. For the followers of Protagoras, as has been stated in Book IV (344:C 637), said that things are such because we so perceive them or judge about them. Therefore, although they say nothing extraordinary or important, they nevertheless seem to be saying something of consequence, because they covertly insinuate their doctrine.
lib. 10 l. 2 n. 24 Deinde cum dicit quod quidem epilogat quae dicta sunt; scilicet quod de ratione unius est, quod sit mensura. Et hoc maxime proprium est, prout est in quantitate; deinde in qualitate, et in aliis generibus; quia id quod est mensura, debet esse indivisibile, aut secundum quantitatem, aut secundum qualitatem. Et ita sequitur, quod unum sit indivisibile, aut simpliciter, sicut unitas, quae est principium numeri, aut secundum quid, idest inquantum est unum, ut dictum est in aliis mensuris.	1960. It is evident (828). Then he sums up the points discussed, namely, that the notion of unity involves being a measure; and this applies most properly to quantity, and then to quality and to the other genera, because anything that is a measure should be indivisible either in quantity or in quality. Thus it follows that unity is indivisible, “either in an unqualified sense” as the unit which is the basis of number, or “in a qualified sense,” i.e., to the extent that it is one, as was stated with regard to the other measures.