Authors/Thomas Aquinas/posteriorum/L2/Lect1

Lecture 1 Whether the definition which signifies the quod quid of a thing can be demonstrated

Latin	English
	BOOK II Lecture 1 (89b21-90a35) EACH OF THE FOUR QUESTIONS WHICH PERTAIN TO SCIENCE IS ONE WAY OR ANOTHER A QUESTION OF THE MIDDLE
lib. 2 l. 1 n. 1 Postquam philosophus in primo libro determinavit de syllogismo demonstrativo, in hoc libro intendit determinare de principiis eius. Est autem duplex principium demonstrativi syllogismi, scilicet medium eius et primae propositiones indemonstrabiles. Dividitur ergo liber iste in duas partes: in prima, determinat de cognitione medii in demonstrationibus; in secunda, de cognitione primarum propositionum; ibi: de principiis autem qualiter fiunt cognita et cetera. Quia enim in primo libro habitum est quod omnis doctrina et omnis disciplina fit ex praeexistenti cognitione; in demonstrationibus autem cognitio conclusionis acquiritur per aliquod medium et per primas propositiones indemonstrabiles; residuum erat investigare qualiter ista innotescant.	After determining about the demonstrative syllogism in the first book, the Philosopher intends in this [second] book to treat concerning its principles. But there are two principles of the demonstrative syllogism, namely, its middle and the first indemonstrable propositions. Therefore this book is divided into two parts. In the first he determines concerning the knowledge of the middle in demonstrations. In the second concerning the knowledge of the first propositions (99b18) [L. 20]. For since it has been established in the first book that every doctrine and every discipline takes its start from pre-existing knowledge, and since in demonstrations the knowledge of the conclusion is acquired through some middle and through the first indemonstrable propositions, we are left with the task of investigating how these come to be known.
Prima autem pars dividitur in duas partes: in prima, investigat quid sit medium in demonstrationibus; in secunda parte inquirit quomodo illud medium nobis innotescat; ibi: quomodo autem quod quid est ostenditur et cetera. Quia vero medium in demonstrationibus assumitur ad aliquid innotescendum de quo poterat esse dubitatio vel quaestio, ideo circa primum duo facit: primo enim, ponit numerum quaestionum; secundo, ex ipsis quaestionibus investigat propositum, ostendens qualiter quaestiones pertineant ad medium demonstrationum; ibi: quaerimus autem cum quaeramus et cetera. Circa primum tria facit: primo, enumerat quaestiones; secundo, manifestat compositas quaestiones; ibi: cum quidem enim utrum hoc etc.; tertio, simplices; ibi: quaedam autem alio modo et cetera.	But the first part is divided into two parts. In the first he inquires what is a middle in demonstrations. In the second part he inquires how that middle is made known to us (90a36) [L. 2]. But because the middle in demonstrations is employed in order to make known something about which there might have been doubt or question, therefore in regard to the first he does two things. First, he lays down the number of questions. Secondly, from these questions he pursues his investigation by showing how the questions pertain to the middle of demonstrations (89b38). Regarding the first he does three things. First, he enumerates the questions. Secondly, he explains complex questions (89b26). Thirdly, simple questions (89b32).
lib. 2 l. 1 n. 2 Dicit ergo primo quod aequalis est numerus quaestionum et eorum quae sciuntur. Cuius ratio est, quia scientia est cognitio per demonstrationem acquisita. Eorum autem oportet per demonstrationem cognitionem acquirere, quae ante fuerint ignota: et de his quaestiones facimus, quae ignoramus. Unde sequitur quod ea quae quaeruntur sint aequalia numero his quae sciuntur. Quatuor autem sunt quae quaeruntur, scilicet quia, propter quid, si est et quid est: ad quae quatuor reduci potest quidquid est quaeribile vel scibile.	He says therefore first (89b21) that the number of questions is equal to the number of things that are scientifically known. The reason for this is that science is knowledge acquired through demonstration. But things which we previously did not know are those of which we must seek knowledge by demonstration: for it is in regard to things which we do not know that we form questions. Hence it follows that the things we inquire about are equal in number to the things we know through science. But there are four things that we ask, namely, quia [i.e., is it a fact that], propter quid [i.e., why, or what is the cause or reason], si est [if it is, i.e., whether it is], quid est [what is it]. To these four can be reduced whatever is scientifically inquirable or knowable.
Dividit autem in I topicorum quaestiones sive problemata aliter in quatuor, quae omnia comprehenduntur sub una harum quaestionum, quae dicitur quaestio quia. Non enim ibi intendit nisi de quaestionibus ad quas dialectice disputatur.	However in Topics I he divides questions or problems into four kinds in a different way, but all of them are included under one of the questions listed here, namely, the one called quia. For in the Topics he is concerned only with questions to be disputed dialectically.
lib. 2 l. 1 n. 3 Deinde cum dicit: cum quidem enim utrum hoc etc., manifestat propositas quaestiones, et primo compositas. Ad cuius evidentiam considerandum est quod, cum scientia non sit nisi veri, verum autem significetur solum per enunciationem, oportet solam enunciationem esse scibilem, et per consequens quaeribilem. Sicut autem in II perihermeneias dicitur, enunciatio dupliciter formatur. Uno quidem modo, ex nomine et verbo absque aliquo apposito, ut cum dicitur homo est; alio modo, quando aliquid tertium adiacet, ut cum dicitur homo est albus.	Then (89b26) he clarifies the questions he laid down; and first of all the complex ones. To understand this it should be noted that science bears only on the true, and the true is not signified except by an enunciation; therefore, only the enunciation can be scientifically knowable and so inquirable. But, as it is stated in On Interpretation II, the enunciation is formed in two ways: in one way from a name and a verb without an appositive, as when it is stated that man is; in another way when some third item is set adjacent, as when it is stated that man is white.
Potest igitur quaestio formata referri, vel ad primum modum enunciationis, et sic erit quasi quaestio simplex; vel ad secundum modum, et sic erit quaestio quasi composita, vel in numerum ponens, quia videlicet quaeritur de compositione duorum.	Therefore the questions we form can be reduced either to the first type of enunciation so that we get, as it were, a simple question; or to the second type, and then the question will be, as it were, complex or put in number, because, namely, the question concerns the putting together of two items.
Circa hunc ergo modum enunciationis duplex quaestio formari potest. Una quidem, an hoc sit verum quod dicitur. Et hanc quaestionem primo exponit, dicens quod cum de aliqua re quaerimus utrum illa res sit hoc aut illud, et sic quodammodo ponimus in numerum (accipiendo scilicet duo, quorum unum est praedicatum et aliud subiectum; puta cum quaerimus utrum sol sit deficiens per eclipsim vel non, et utrum homo sit animal vel non), tunc dicimur quaerere quia: non ita quod hoc quod dico quia sit nota vel signum interrogationis, sed quia ad hoc quaerimus ut sciamus quia ita est. Cuius signum est, quia cum invenerimus per demonstrationem, quiescimus a quaerendo; et si in principio hoc scivissemus, non quaereremus utrum ita sit. Inquisitio autem non cessat, nisi habito eo quod quaerebatur. Et ideo cum quaestio qua quaerimus utrum hoc sit hoc, cesset habito quod ita est, manifestum est quid huiusmodi quaestio quaerit.	According to this latter type a twofold question can be formed: one of them is whether this is true which is stated. This question he expounds first, saying that when we ask concerning some thing whether that thing is this or that, so that in effect we are somehow putting it in number, namely, by taking two things one of which is predicate and the other subject, as when we ask if the sun is failing because of an eclipse or not, and is man an animal or not, then we are said to ask quia: not in the sense that the word “quia” functions as a question mark, but because we are asking in order to find out quia [i.e., that] it is so. An indication of this is that when we have discovered it through demonstration, we cease our questioning; and if we had known it at the very beginning, we would not have asked whether it is so. But inquiry does not cease until that is obtained which was asked. And so, since the question in which we ask whether this is this ceases once we have certified that it is so, it is clear what a question of this kind asks.
lib. 2 l. 1 n. 4 Deinde cum dicit: cum autem scimus etc., manifestat consequentem quaestionem, quae etiam in numerum ponit; et dicit quod cum scimus quia ita est, quaerimus propter quid ita sit. Puta, cum scimus quia sol est deficiens per eclipsim, et quod terra est mota in terraemotu, quaerimus propter quid sol deficiat, aut propter quid terra moveatur. Hoc igitur sic quaerimus, ponentes scilicet in numerum.	Then (89b28) he clarifies the next question which also puts in number, ‘I saying that when we know that it is so, we ask propter quid [i.e., why] it is so. For example, when we know that the sun is failing through an eclipse and that the earth is moved during an earthquake, we ask why the sun is failing or why the earth is being moved. Therefore we ask it in this way, namely, by putting in number.
lib. 2 l. 1 n. 5 Deinde cum dicit: quaedam autem alio modo etc., manifestat alias duas quaestiones, quae non ponunt in numerum, sed sunt simplices. Et dicit quod quaedam quaerimus alio modo a praedictis quaestionibus, scilicet non ponentes in numerum; utpote si quaeramus an sit Centaurus vel non: hic enim simpliciter quaeritur de Centauro an sit, non autem quaeritur an Centaurus sit hoc, puta album vel non. Et sicut scientes quia hoc est illud, quaerebamus propter quid, ita etiam scientes de aliquo quia est simpliciter, quaerimus quid sit illud, puta quid est Deus, aut quid est homo. Haec igitur et tot sunt illa quae quaerimus: quae cum invenerimus, dicimur scire.	Then (89b32) he clarifies the other two questions which do not put in number but are simple. And he says that we ask certain things in a manner different from the aforesaid questions, namely, by not putting in number; as when we ask whether or not there be centaurs, for in this case the question we ask concerning the centaur is simply whether it exists and not whether the centaur be this, say white, or not. And just as when we knew that this is this, we then asked why, so once we know of something simply that it is, we ask what it is, for example, what is God or what is man. These then and so many are the things we ask; and when we have found the answer, we are said to know scientifically.
lib. 2 l. 1 n. 6 Deinde cum dicit: quaerimus autem cum quaeramus etc., ostendit qualiter praedictae quaestiones se habeant ad medium. Et circa hoc tria facit: primo, proponit quod intendit; secundo, manifestat quod dixerat; ibi: dico autem quia etc.; tertio, probat propositum; ibi: contingit itaque in omnibus quaestionibus et cetera.	Then (89b38) he shows how the aforesaid questions are related to the middle. Concerning this he does three things. First, he states what he intends. Secondly, he explains what he had said (90a2). Thirdly, he proves his proposition (90a5).
Circa primum sciendum est quod praedictarum quatuor quaestionum, quarum duae ponunt in numerum et duae non ponunt, primam utrarumque in unam coordinat, scilicet quaestionem quia et quaestionem an est. Et dicit quod cum quaerimus quia hoc est hoc, aut cum quaerimus de aliquo simpliciter si est, nihil aliud quaerimus quam utrum aliquod medium ipsius quod quaerimus sit invenire vel non. Quod non dicitur secundum ipsam formam quaestionis. Non enim cum quaero an sol eclipsetur, vel an homo sit, ex ipsa forma quaestionis quaero an sit aliquod medium, quo possit demonstrari vel solem eclipsari, vel hominem esse: sed si sol eclipsatur, vel homo est, consequens est quod sit aliquod medium invenire ad demonstrandum ista quae quaeruntur. Non enim fit quaestio de immediatis, quae etsi vera sunt, non tamen habent medium; quia huiusmodi, cum sint manifesta, sub quaestione non cadunt. Sic ergo qui quaerit an hoc sit hoc, vel an hoc sit simpliciter, ex consequenti quaerit an sit huiusmodi medium. Quaeritur enim in quaestione si est, vel quia est, an sit id quod est medium; quia id quod est medium est ratio eius, de quo quaeritur an hoc sit hoc, vel an simpliciter, ut infra dicetur. Non tamen quaeritur sub ratione medii.	In regard to the first it should be noted that two of the aforesaid questions put in number and two do not. From the first member of each of these groups, he forms another grouping composed of the question that it is and the question if it is. And he says that when we ask that this is this, or when we simply ask concerning something, if it is, we are not asking anything else than whether or not a middle is to be found of that which we ask; and this is something not conveyed by the form of the question. For when I ask whether the sun is eclipsed or whether man exists, it is not obvious from the form of the question that I am asking whether there is some middle by which it might be demonstrated that the sun is eclipsed or that man exists; but if the sun is eclipsed or man does exist, the consequence is that some middle can be found to demonstrate the things which are inquired. For no one forms a question concerning immediate things which, although they are true, do not have a middle, since things of this sort, being evident, do not fall under a question. Thus, therefore, one who asks whether this is this or whether this absolutely is, as a consequence is asking whether there is a middle of this sort. For in the question if it is or that it is, one is asking whether that which is a middle exists, because that which is the middle is the reason of that concerning which one asks whether this is this or simply whether it is, as will be explained below. Nevertheless the question is not being asked under the aspect of middle.
Contingit autem, invento quod quaeritur per has duas quaestiones, cognoscere aut quia est aut si est: quorum alterum est cognoscere esse simpliciter, alterum esse in parte, sicut cum cognoscimus quod homo est albus; quia esse album non significat totaliter esse hominis, sed significat ipsum esse aliquid; et ideo cum homo fit albus, non dicitur generari simpliciter, sed generari secundum quid. Sed cum dicitur, homo est, significatur ipsum esse simpliciter; et cum homo fit ens, dicitur generari simpliciter.	Now it happens that having found the answer to what is asked by these two questions, one knows either that it is or if it is: one of which consists in knowing the existence absolutely; but the other in part, as when we know that man is white, because to be white does not signify the existence of man in his entirety but signifies him to be something. This is why when a man is becoming white, we do not say that he is coming to be absolutely, but in a qualified sense. But when it is asserted that man is, his existence is signified absolutely, so that when a man comes to be, he is said to become absolutely.
Cum ergo cognito quia est, quaerimus propter quid est, aut cognito si est, quaerimus quid est, tunc quaerimus quid sit medium. Et hoc similiter est accipiendum non secundum formam quaestionis, sed secundum concomitantiam. Non enim qui quaerit causam propter quam sol eclipsatur, quaerit ipsam ut medium demonstrans, sed quaerit id quod est medium: quia consequens est ut, hoc habito, possit demonstrare. Et eadem ratio est de quaestione quid est.	Therefore, when we know that it is and ask why it is, or when we know if it is and ask what it is, we are asking what is the middle. And as in the other cases, so here, this is gathered not from the form of the question but by way of concomitance. For one who seeks the cause why the sun is eclipsed is not seeking it as a middle which demonstrates, but he is seeking that which is a middle, because it is by way of consequence that once he has it, he can demonstrate. And the same applies to the question what is it.
lib. 2 l. 1 n. 7 Deinde cum dicit: dico autem quia aut si est etc., manifestat quod dixerat, quod quia est et si est differunt sicut in parte et simpliciter. Cum enim quaerimus utrum deficit luna aut utrum augetur, est quaestio in parte: in huiusmodi enim quaestione quaerimus si luna est aliquid; puta si deficiens, vel aucta, aut non. Sed cum quaerimus an luna sit, sive an nox sit, est quaestio de esse simpliciter.	Then (904) he manifests what he had said, namely, that that it is and if it is differ as in part and absolutely differ. For when we inquire whether the moon is waning or waxing, it is a question in part, since in a question of this type we are asking if the moon is something, namely, is it waning or has it waxed or not. But when we ask whether the moon exists or whether it is night, the question bears on existence absolutely.
lib. 2 l. 1 n. 8 Deinde cum dicit: contingit itaque in omnibus etc., probat propositum, scilicet quod praedictae quaestiones pertineant ad medium. Et primo, probat per rationem; secundo, probat per signum; ibi: quod autem sit medii et cetera.	Then (90a5) he proves his point, namely, that the aforesaid questions pertain to the middle. First, he proves it with a reason. Secondly, with a sign (90a24).
Concludit ergo primo ex praemissa manifestatione quod in omnibus praedictis quaestionibus, vel quaeritur an sit medium, scilicet in quaestione quia et in quaestione si est; vel quaeritur quid est medium, scilicet in quaestione propter quid et in quaestione quid est.	He concludes therefore first (90a5) from the explanation given above that in all the aforesaid questions one is either asking whether there is a middle, namely, in the question that it is and in the question if it is, or what the middle is, namely, in the question why and in the question what is it.
Et probat quod quaestio propter quid quaerat quid sit medium. Manifestum est enim quod causa est medium in demonstratione, quae facit scire; quia scire est causam rei cognoscere. Causa autem est quod quaeritur in omnibus praedictis quaestionibus. Quod primo manifestat in quaestione quia. Cum enim quaeritur utrum luna deficiat, quaeritur secundum modum supra expositum, utrum aliquid sit causa defectus lunae vel non. Et consequenter hoc manifestat in quaestione propter quid. Cum enim scimus quia est aliquid causa defectus lunae, quaeritur quid sit causa; et hoc est quaerere propter quid.	And he proves that the question why inquires what the middle is. For it is obvious that a cause is the middle in a demonstration which enables one to know scientifically, because to know scientifically is to know the cause of a thing. But it is precisely the cause that is being sought in all the above questions. That this is so he manifests first in regard to the question that. For when it is asked whether the moon is waning, then according to the manner explained above, what is being asked is whether or not something is the cause of this waning. Then he shows this for the question why. For once we know that something is the cause of the moon’s waning, we ask what the cause is; and this is to inquire why.
Et eadem ratio est in aliis duabus quaestionibus, ut per sequentia manifestat. Dicit enim quod, sive accipiamus aliquam rem esse non hoc aut hoc (puta cum dico homo est albus, aut grammaticus), sed accipiamus ipsam substantiam esse simpliciter; sive etiam non accipiamus rem aliquam esse simpliciter, sed rem aliquam esse aliquid, ponendo in numerum, (sive illud aliquid sit de numero eorum quae praedicantur per se, sive de numero eorum quae praedicantur per accidens), sive hoc modo sive illo accipiamus rem esse, causa eius est medium ad demonstrandum ipsam.	The same applies to the other two questions, as he shows in the following way. For he says that whether we assert not that something is this or that (for example, when I say that man is white or is a grammarian), but that the substance itself exists absolutely; or do not assert that some thing exists absolutely, but that some thing is something by putting in number (whether that something be a thing predicated per se or a thing predicated per accidens); no matter in which of these ways we take the thing to be, its cause is the middle for demonstrating it.
Exponit autem consequenter quod dixit, simpliciter substantiam esse, cum quaerimus de luna, aut de terra, aut de triangulo, aut de quolibet subiecto an sit, et ad hoc demonstrandum accipitur aliquod medium. Dico autem rem esse aliquid, cum quaerimus eclipsim de luna, aut aequalitatem, aut inaequalitatem de triangulo, aut de terra utrum sit in medio mundi vel non. Et ostendit quod non differt quantum ad propositum utrolibet modo accipiatur rem esse; quia in omnibus praedictis idem est quid est et propter quid.	Then he explains what he means by a substance to exist absolutely when we inquire concerning the moon or the earth or a triangle or any other subject whether it is and then take some middle to demonstrate this. I say that a thing is something when we inquire concerning eclipse in regard to the moon, or equality or inequality in regard to triangle, or whether it is in the middle of the universe or not in regard to the earth. And he asserts that as far as the present point is concerned it makes no difference which way a thing is taken to be, because in all these cases what it is is the same as why.
Et hoc manifestat primo in defectu lunae. Si enim quaeratur quid est defectus lunae: respondetur quod est privatio luminis a luna propter terram, quae obiicitur inter ipsam et solem. Et hoc idem respondemus si quaeratur propter quid luna deficit. Dicimus enim quod luna deficit propter defectum luminis ex oppositione terrae.	He manifests this first of all in regard to the waning, of the moon. For if one asks what is the eclipse of the moon, the answer is that it is the absence of light in the moon because of the earth’s being set between it and the sun. And this same answer is given when it is inquired why the moon is eclipsed. For we say that the moon is eclipsed because there is a lack of light due to the earth’s opposition.
Et idem manifestat in alio exemplo. Si enim quaeratur quid est consonantia: respondetur quod est ratio, idest proportio numerorum secundum acutum et grave. Et rursum si quaeratur propter quid acutum consonat gravi: respondetur propter id quod habent numeralem proportionem acutum et grave. Sic ergo quaestio quid est et quaestio propter quid redeunt in idem subiecto, quamvis differant ratione. Unde quia cum quaeritur propter quid, quaeritur quid sit medium, ut ostensum est, relinquitur quod cum quaeritur quid est, similiter quaeratur medium.	Then he manifests the same idea with another example. For if one asks what is a chord, the answer is given that it is a numerical ratio according to high and low notes. Again, if one asks why a high note and a low note are concordant, the answer is given that it is because the high note and the low note have a numerical ratio. And so the question what is it and the question why reduce to the same thing subjectively, although they differ in formality. Hence because the question why leads us to inquire what the middle is, as has been shown, what is left is that when one asks what is it, the middle is likewise inquired.
Et idem ostendit in quaestione quia. Ut enim dictum est, consonantia est ratio in numeris acuti et gravis: cum ergo quaeritur utrum acutum et grave consonent, quaeritur utrum sit aliqua ratio numeralis acuti et gravis; et hoc est medium ad demonstrandum quod acutum et grave consonant. Relinquitur ergo quod in quaestione quia quaeritur an sit medium. Cum autem acceperimus quia est aliqua ratio numeralis acuti et gravis, quaeremus quae sit illa ratio. Et hoc est quaerere quid vel propter quid.	Then he shows the same thing in regard to the question that. For, as has been said, concordance is a numerical ratio between high and low notes. Men, therefore, one asks whether a high and low note concord, he is inquiring whether there is some numerical ratio of the high and low note; and this is the middle for demonstrating that a high and a low note concord. Consequently in the question that, one inquires whether there is a middle. But once we have found that there is a numerical ratio of the high and low note, we then ask what that ratio is: and this is to ask what or why.
lib. 2 l. 1 n. 9 Videtur hic Aristoteles dicere quod definitio passionis sit medium in demonstratione. Sed considerandum est quod definitio passionis perfici non potest sine definitione subiecti. Manifestum est enim quod principia, quae continet definitio subiecti, sunt principia passionis. Non ergo demonstratio resolvet in primam causam, nisi accipiatur ut medium demonstrationis definitio subiecti. Sic igitur oportet concludere passionem de subiecto per definitionem passionis, et ulterius definitionem passionis concludere de subiecto per definitionem subiecti. Unde et in principio dictum est quod oportet praecognoscere quid est, non solum de passione, sed etiam de subiecto; quod non oporteret nisi definitio passionis concluderetur de subiecto per definitionem subiecti.	Here Aristotle seems to say that the definition of a proper attribute is the middle in demonstration. However it must be remarked that the definition of the proper attribute cannot be completed without the definition of the subject. For it is obvious that the principles which the definition of the subject contains are the principles of the proper attribute. Hence a demonstration will not reach the first cause unless one takes as the middle of demonstration the definition of the subject. And so the proper attribute must be concluded of the subject by means of the definition of the proper attribute; furthermore, the definition of the proper attribute must be concluded of the subject through the definition of the subject. This is why it was laid down at the very beginning that one must know beforehand the what is it not only of the proper attribute but of the subject also; which would not be required unless the definition of the proper attribute were concluded of the subject through the definition of the subject.
Et hoc patet per exemplum. Si velimus de triangulo demonstrare quod habet tres angulos aequales duobus rectis, accipiamus primo pro medio quod est figura habens angulum extrinsecum aequalem duobus intrinsecis sibi oppositis, quod est quasi definitio passionis. Quod iterum demonstrare oportet per definitionem subiecti, ut dicamus: omnis figura tribus rectis lineis contenta habet angulum exteriorem aequalem duobus interioribus sibi oppositis; sed triangulus est huiusmodi; ergo et cetera. Et idem patet si velimus demonstrare quod vox acuta et gravis consonent: accipiemus definitionem passionis, ut hic dicitur, scilicet quod habent proportionem numeralem; sed rursus ad hoc demonstrandum oportet accipere definitionem gravis et acuti. Nam gravis vox est quae in multo tempore nata est movere sensum, acuta autem quae in modico tempore; modici autem ad multum est proportio numeralis; ergo vocis acutae et gravis est proportio numeralis. Nec refert si aliter definiatur acutum et grave. Oportet enim in eorum definitione ponere aliquid ad quantitatem pertinens; et sic necesse erit concludere in eis proportionem numeralem.	This is clear from the following example: If we wish to demonstrate of triangle that it has three angles equal to two right angles, we first take as middle the fact that it is a figure having an exterior angle equal to its two opposite interior angles-which is, as it were, the definition of a proper attribute. But this in turn must be demonstrated by the definition of the subject, so that we would say: “Every closed figure of three straight lines has an exterior angle equal to its two opposite interior angles; but the triangle is such a figure. Therefore...” And the same is true if we were to demonstrate that a high note concords with a low note: for we would state the definition of the attribute which in this case consists in their having a numerical ratio; but then to demonstrate this attribute we would have to take the definition of high note and of low note. For a low note is one which is apt to act on the sense for a long time, whereas a high note is one which does so for a short time: but between the long and the short there is a numerical ratio. Therefore, there is a numerical ratio between a high note and a low note. And if the high note and the low note were defined some other way, it would make no difference. For in any case something pertaining to quantity would have to appear in their definition, so that it would be necessary to conclude that there is a numerical ratio between them.
lib. 2 l. 1 n. 10 Deinde cum dicit: quod autem medii sit quaestio etc., ostendit propositum per signum sensibile. Et dicit quod ea in quibus medium est sensibile, manifeste ostendunt quod omnis quaestio sit quaestio medii: quia scilicet quando medium per sensum innotescit, nullus relinquitur quaestioni locus. Tunc enim quaerimus in rebus sensibilibus secundum aliquam praedictarum quaestionum, quando medium non sentimus: sicut quaerimus an sit defectus lunae vel non, quia non sentimus medium quod est causa faciens deficere lunam. Sed si essemus in loco qui est super lunam, videremus quomodo luna subintrando umbram terrae deficeret; et ideo circa hoc nihil quaereremus, nec si est nec propter quid est; sed simul utrumque nobis fieret manifestum.	Then (90a44) he manifests his point by means of a sensible sign. And he says that those cases in which the middle is perceptible by sense clearly show that every question is a question concerning a middle, because, namely, when the middle is known through the senses, no room is left for a question. For we ask one of the aforesaid questions in matters pertaining to sense, when the middle does not appear: thus, we ask whether or not there is an eclipse of the moon because we do not sensibly perceive the middle which is the cause making the moon to be eclipsed. But if we were to situate ourselves in a place above the moon, we would see how the moon became eclipsed by entering the earth’s shadow. Then we would no longer ask if it is or why it is, but both would at once be obvious to us.
lib. 2 l. 1 n. 11 Et quia posset aliquis obviando dicere quod sensus est singularium, ea vero quae quaeruntur sunt universalia, sicut et ea quae sciuntur; et ita per sensum non videtur quod possit nobis innotescere id de quo est quaestio: ideo quasi obviationi respondens subiungit quod ex hoc ipso quod sentiremus particulare, scilicet quod, hoc corpus lunae tunc subintrat hanc umbram terrae, statim accideret nobis quod sciremus universale. Sensus enim noster esset de hoc quod nunc lumen solis obstruitur per oppositionem terrae; et per hoc manifestum esset nobis quod luna nunc deficit. Et quia nos coniiceremus quod semper hoc modo accideret lunae defectus, statim in nostra scientia sensus rei singularis fieret universale.	But because someone could object that sense-perception bears on singulars—whereas it is universals that are being asked about, just as it is universals that are scientifically known—and consequently, it does not seem that the matter under question can be made known through sense; therefore, as though in answer to this objection he adds that it is precisely because we do sense the particular (namely, that this body of the moon enters this shadow of the earth), that we happen at once to know the universal. For our sense would observe the fact that the light of the sun is now blocked by the earth’s opposition; and through this it would be clear to us that the moon is now eclipsed. And because we would conjecture that the eclipse of the moon always occurs in this way, the sense knowledge of the singular would immediately become a universal in our science.
Et ex hoc exemplo concludit quod idem est scire quod quid est et propter quid. Nam ex hoc quod videmus terram interpositam inter solem et lunam, sciremus et quid est defectus lunae et propter quid luna deficit: quorum unum, scilicet scire quid est, refertur ad scientiam qua scimus de aliquo quod simpliciter sit, non autem quod aliquid insit alicui; sed propter quid refertur ad cognitionem eorum quae insunt, sicut cum dicimus quod tres anguli sunt aequales duobus rectis, aut maiores aut minores. Ultimo autem epilogando concludit principale propositum, scilicet manifestum esse ex praedictis, in omnibus quae quaeruntur esse medii quaestionem.	And so from this example he concludes that knowing the quod quid [quod quid refers to any or all of the items that constitute the essential nature of a thing.] and the why are the same. For from the fact that we observe the earth situated between the sun and moon, we would know scientifically both what an eclipse of the moon is and why the moon is eclipsed. And one of these, namely, the knowledge what it is, is reduced to the science by which we know that something simply is, and not that something is in some thing. But the why is reduced to our knowledge of things that are in some thing, as when we say that three angles are equal to or greater than or less than two right angles. Finally, he summarizes and concludes the main point, namely, that it is clear from the foregoing that in all questions there is question of the middle.