Authors/Thomas Aquinas/posteriorum/L1/Lect36

Lecture 36 Certain corollaries from preceding lectures

Latin	English
	Lecture 36 (84b3-85a11) CERTAIN COROLLARIES FROM PRECEDING LECTURES
lib. 1 l. 36 n. 1 Postquam philosophus ostendit quod non contingit procedere in infinitum in demonstrationibus, hic inducit quaedam corollaria ex dictis. Et circa hoc duo facit: primo, ostendit quod necesse est accipere aliquas primas propositiones; secundo, quomodo illis primis sit utendum in demonstrationibus; ibi: cum autem oportet demonstrare et cetera. Circa primum duo facit: primo, ostendit quod necesse est devenire ad aliquod primum, quando unum de pluribus praedicatur; secundo, quando unum praedicatur de uno; ibi: manifestum autem et cetera. Circa primum quatuor facit: primo, proponit intentum; secundo, manifestat propositum; ibi: ut scaleno etc.; tertio, probat; ibi: sit autem b etc.; quarto, excludit quamdam obviationem; ibi: in eodem quidem genere et cetera.	After showing that a process to infinity does not occur in demonstrations, the Philosopher here adduces certain corollaries from what has been established. In regard to this he does two things. First, he shows that it is necessary to accept certain first propositions. Secondly, how those first things are to be used in demonstrations (8032). Concerning the first he does two things. First, he shows that it is necessary to arrive at a first, when one thing is predicated of several. Secondly, when one thing is predicated of one (84b19). In regard to the first he does four things. First, he states the intended proposition. Secondly, he manifests the proposition (84b6). Thirdly, he proves it (84b9). Fourthly, he excludes an objection (84b15).
lib. 1 l. 36 n. 2 Dicit ergo primo, quod demonstratis praemissis, scilicet quod non sit procedere in infinitum in praedicationibus et demonstrationibus, manifestum est quod si aliquid praedicatur de duobus, puta a de c et d, ita scilicet quod unum eorum non praedicetur de altero, aut nullo modo, sicut animal praedicatur de homine et bove, quorum unum nullo modo de alio praedicatur, aut non de omni, puta animal praedicatur de homine et masculo, quorum neutrum de altero universaliter praedicatur; sic, inquam, se habentibus terminis, manifestum est quod non oportet quod illud praedicatum, quod de utroque praedicatur, insit utrique secundum aliquod commune, et hoc semper, idest in infinitum procedendo.	He says therefore first (84b3) that having demonstrated the aforesaid, namely, that there is no process to infinity in predications and demonstrations, it is clear that if something is predicated of two things, say A of C and of D, such that one of them is not predicated of the other, i.e., either not at all, as animal is predicated of man and ox, but neither of them is predicated of the other in any way; or not in all cases, as animal is predicated of man and male, neither of which is universally predicated of the other: when the terms, I repeat, are thus related, it is clear that there is no need for that predicate, which is predicated of both, to be in them in virtue of something common to both and this again in virtue of something else, and so on to infinity.
lib. 1 l. 36 n. 3 Deinde cum dicit: ut scaleno et isosceli etc., manifestat propositum per exemplum. Sunt enim duae species trianguli, quarum una vocatur scalenon, vel triangulus gradatus, cuius sunt tria latera inaequalia; alia est isosceles, cuius sunt duo latera aequalia: unum autem horum non praedicatur de altero; utrique autem inest haec passio, habere tres angulos aequales duobus rectis. Inest autem hoc eis secundum aliquid commune, scilicet secundum quod uterque horum est figura quaedam, scilicet triangulus. Hoc autem non semper sic se habet, scilicet quod in infinitum conveniat secundum aliquid aliud; puta quod habere tres conveniat triangulo iterum secundum aliquid aliud, et sic in infinitum.	Then (806) he cites an example to clarify what he is proposing. For there are two species of triangle, one of which is scalene (none of whose three sides is equal to any other) and the other is isosceles (having two sides that are equal). But neither of these species is predicated of the other, and yet this proper attribute of having three angles equal to two right angles is present in both. Furthermore, this attribute is present in them in virtue of something common, namely, that each is a certain figure, namely, a triangle. However, this process does not continue forever so that something would always belong to it in virtue of something else and so on to infinity, so that “having three” would belong to triangle in virtue of something else again, and so on to infinity.
lib. 1 l. 36 n. 4 Deinde cum dicit: sit enim b secundum etc., probat propositum et dicit: sit ita quod b praedicetur de c et de d secundum hoc commune, quod est a. Manifestum est ergo quod b erit in c et in d secundum illud commune, quod est a; et si iterum insit a secundum aliquod commune, et iterum illi communi secundum aliquid aliud, procedetur in infinitum in mediis. Sequitur igitur quod inter duo extrema, quae sunt c et b, cadant infiniti termini medii. Hoc autem est impossibile: ergo non necesse est, si idem insit pluribus, quod semper in infinitum insit eis secundum aliquid commune; quia necesse est quod deveniatur ad aliqua spatia immediata, idest ad aliquas immediatas praedicationes, quas appellat spatia, ut supra dictum est.	Then (84b9) he proves his proposition and says: Let the case be that B is predicated of C and of D in virtue of this common feature A. It will then be clear that B will be in C and in D in virtue of that common feature which is A. Now if A in turn is in them in virtue of something common, which again is in them in virtue of some other common item, there will be an infinite process in the middles. It follows, therefore, that between the two extremes C and B there falls an infinitude of middle terms. But this is impossible. Therefore, if a same thing is in several things, it is not necessary that it be in them always in virtue of something else ad infinitum, because it is necessary to reach certain “immediate distances,” i.e., certain immediate predications, which he calls “distances,” as explained above.
lib. 1 l. 36 n. 5 Quantum igitur videtur ex hac probatione Aristotelis, non est suus intellectus, quod hoc non semper sit verum, quod quando aliquid praedicatur de pluribus, quae de se invicem non praedicantur, quod illud non insit illis pluribus secundum aliquid commune. Hoc enim verum est in omni quod praedicatur sicut passio: oportet enim si inest pluribus, quod insit eis secundum aliquid commune, licet forte illud sit innominatum, sicut supra dictum est cum de universali ageretur. Sed in illo communi non proceditur in infinitum, ut haec ratio inducta a philosopho evidenter probat. Si autem accipiatur aliquid, quod insit pluribus sicut genus speciebus, non semper oportebit aliquid prius accipere, secundum quod insit, puta si vivum insit homini et asino secundum aliquod prius, scilicet secundum animal; animali autem et plantae non inest secundum aliquod prius, quia haec sunt primae species corporis vivi, sive animati.	As can be seen from this proof of Aristotle’s, it is not his understanding that it is not always true that when some item is predicated of several, which are not in turn predicated of one another, that item is not in the several in virtue of something common. For this is true in everything predicated as a proper attribute: for if it is in several, it is required that it be in them in virtue of something common which might even be nameless, as we explained above when we treated concerning the universal. But there is no infinite process in that which is common, as this reason introduced by the Philosopher clearly proves. However, if something be taken which is in several as a genus in its species, it will not always be necessary to find something prior in virtue of which it is in them. For example, “living” is in man and in ass in virtue of something prior, namely, in virtue of “animal,” but it is not in animal and plant in virtue of something prior, because these are the first species of “living,” i.e., of animate, body.
lib. 1 l. 36 n. 6 Deinde cum dicit: in eodem quidem genere etc., excludit quamdam obviationem. Posset enim aliquis dicere quod semper accipitur secundum aliquid commune, quia potest accipi commune alterius generis: puta si dicamus quod esse seipsum movens inest homini et asino secundum hoc commune, quod est animal, et secundum aliud commune, quod est habens quantitatem, vel habens colorem, aut aliquid aliud huiusmodi; quae possunt accipi in infinitum.	Then (84b15) he excludes an objection. For someone could say that it is always taken in virtue of something common, in the sense that something from another genus might be found common to them: for example, if we say that “to be self-movent” is in man and in ass in virtue of this common feature which is “animal” and also in virtue of some other common feature such as “having quantity” or having color or other things of this sort that can be taken ad infinitum.
Et ad hoc excludendum dicit, quod necesse est terminos medios, qui accipiuntur, accipi ex eodem genere et ex eisdem atomis, idest indivisibilibus. Et appellat atomos, ipsos terminos extremos: inter quos oportet accipi medium, si illud commune, quod accipitur ut medius terminus, sit de numero eorum, quae praedicantur per se. Quare autem oporteat ex eodem genere assumere terminos medios, ostendit per hoc, quod sicut supra habitum est, non contingit demonstrationem transire de uno genere in aliud.	In order to exclude this he says that it is required of the middle terms that they be taken from the same genus and “from the same atoms,” i.e., indivisibles. (By “atoms” he means those extreme terms between which the middle must be taken, if that common item which is taken as a middle term is to be numbered among things which are predicated per se). Why the middle terms must be taken from the same genus he shows from the fact that, as stated above, a demonstration does not cross from one genus into another.
lib. 1 l. 36 n. 7 Deinde cum dicit: manifestum autem est etc., ostendit quod necesse est devenire ad aliquod unum in praedicabilibus, in quibus praedicatur unum de uno. Et primo, in affirmativis; secundo, in negativis; ibi: similiter autem et si a et cetera. Dicit ergo primo, manifestum esse quod cum a praedicatur de b, si horum sit aliquod medium, quod illo medio uti possumus ad demonstrandum quod a sit in b: et haec sunt principia huiusmodi conclusionis. Et quaecunque accipiuntur ut media, sunt principia conclusionum mediatarum, quae per ea concluduntur. Nihil enim aliud sunt elementa, sive principia demonstrationum, quam propositiones immediatae.	Then (84b19) he shows that it is necessary to arrive at a first among the predicables in which one thing is predicated of one. First, in affirmatives. Secondly, in negatives (84b24). He says therefore first (84b19) that it is clear that when A is predicated of B, if there is a middle between them, we can use that middle to demonstrate that A is in B: and these are the principles of this kind of conclusion. And what things soever be taken as middles are the principles of the mediate conclusions which are concluded through them. For the “elements” or principles of demonstrations are none but immediate propositions: and I mean “either all such propositions or universal ones.”
Et hoc dico vel omnes, vel universales: quod quidem potest dupliciter intelligi. Uno modo, ut propositio universalis accipiatur secundum quod dividitur contra singularem. Nam species specialissima non praedicatur de singulari per aliquod medium. Unde haec propositio est immediata: Socrates est homo, non tamen est principium demonstrationis, quia demonstrationes non sunt de singularibus, cum eorum non sit scientia: et ita non omnis propositio immediata est demonstrationis principium, sed solum universalis. Alio modo potest intelligi secundum quod propositiones universales dicuntur propositiones communes in omnibus propositionibus alicuius scientiae, sicut, omne totum est maius sua parte: unde huiusmodi sunt simpliciter demonstrationum principia, et omnibus per se nota. Haec autem propositio, homo est animal, vel, isosceles est triangulus, non est principium demonstrationis in tota scientia, sed solum aliquarum particularium demonstrationum; neque etiam huiusmodi propositiones sunt omnibus per se notae.	Now this can be understood in two ways: in one way so that universal proposition is taken as set off against singular. For it is not in virtue of a middle that the most special species is predicated of a singular. Hence this proposition, “Socrates is a man,” is immediate, although it is not a principle of demonstration, because demonstrations are not concerned with singulars, since there is no science of such. Consequently, not every immediate proposition, but only one that is universal, is a principle of demonstration. In another way it can be understood in the sense that of all the propositions of any science, the universal propositions are the common propositions, such as “Every whole is greater than its part.” Hence these are absolutely the principles of demonstrations and self-evident to all. But the proposition, “Man is an animal,” or “The isosceles is a triangle,” is not a principle of demonstration throughout the science but only for some particular demonstrations; hence such propositions are not self-evident to all.
Sic igitur si sit aliquod medium propositionis datae, erit demonstrare per aliquod medium, quousque deveniatur ad aliquod immediatum. Si vero non sit aliquod medium propositionis datae, non poterit demonstrari. Sed haec est via ad inveniendum prima principia demonstrationum, scilicet procedere a mediatis ad immediata resolvendo.	Consequently, if there is a middle for a given proposition, one will demonstrate through a middle until something immediate is readied. But if there is no middle for a given proposition, it cannot be demonstrated. But ihis is the way to find the chief principles of demonstrations, namely, to proceed by analysis from mediates to immediates.
lib. 1 l. 36 n. 8 Deinde cum dicit: similiter autem erit etc., ostendit quod sit accipere primum in negativis; et dicit quod si a negetur de b, si sit accipere aliquod medium, a quo scilicet per prius removeatur a quam a b, tunc haec propositio, b non est a, erit demonstrabilis. Si autem non sit aliquod tale medium accipere, non erit haec propositio demonstrabilis, sed principium demonstrationis. Et tot erunt elementa, idest principia demonstrationis, quot erunt termini; ad quos scilicet statur, ut ultra non sit invenire medium. Propositiones enim quae fiunt ex huiusmodi terminis, sunt principia demonstrationis. Puta si c immediate praedicetur de b, et a immediate removeatur a b, aut praedicetur de eo immediate, b erit terminus ad quem ultimo pervenitur in mediis sumendis: unde utraque propositio erit immediata, et demonstrationis principium.	Then (84b24) he shows that it is necessary to arrive at a first in negatives, saying that if A is denied of B, if there is a middle to be taken from which A is removed prior to being removed from B, then this proposition, “B is not A,” will be demonstrable. But if there is no such middle to be taken, that proposition will not be demonstrable but will be a principle of demonstration. And there are as many “elements,” i.e., principles of demonstrations as there are terms at which a stop is reached in such a way that there is no further middle to find. For propositions formed of such terms are principles of demonstrations. Thus, if C be predicated immediately of B, and A be immediately removed from B or immediately predicated of it, B is the final term reached among the middles to be taken; hence each proposition will be immediate and a principle of demonstration.
Et patet ex praemissis quod sicut sunt quaedam principia indemonstrabilia affirmativa, in quibus unum de alio praedicatur, significando quod hoc essentialiter est illud, sicut cum genus praedicatur de proxima specie, vel hoc sit in illo, sicut cum passio praedicatur de proprio et immediato subiecto; ita etiam sunt principia indemonstrabilia in negativis, negando vel essentiale praedicatum, vel etiam propriam passionem. Ex quo patet quod quaedam sunt principia demonstrationis ad demonstrandum conclusionem affirmativam, quam oportet concludere ex omnibus affirmativis; et quaedam sunt principia demonstrationis ad probandum conclusionem negativam, ad cuius illationem oportet assumere aliquam negativam.	Furthermore, it is clear from the foregoing that just as there are certain indemonstrable affirmative principles in which one thing is predicated of one thing by signifying that this is essentially that (as when a genus is predicated of a proximate species) or that this is in that (as when a proper attribute is predicated of its proper and immediate subject), so there are indemonstrable principles in negatives, namely, by denying that something is an essential predicate or a proper attribute. From this it is evident that there are certain principles of demonstration for demonstrating an affirmative conclusion (which must be concluded from all affirmative propositions), and there are certain principles of demonstration for proving a negative conclusion (to infer which requires that something negative be taken).
lib. 1 l. 36 n. 9 Deinde cum dicit: cum autem oporteat etc., ostendit quomodo utendum sit primis propositionibus in demonstrando. Et primo, in demonstrationibus affirmativis; secundo, in negativis; ibi: in privativis autem et cetera. Circa primum tria facit: primo, ostendit qualiter oporteat sumere propositiones primas et immediatas in demonstrationibus; secundo, ostendit quomodo huiusmodi propositiones se habeant ad demonstrationes; ibi: et quemadmodum in aliis etc.; tertio, epilogat; ibi: in ostensivis quidem igitur et cetera.	Then (84b32) he shows how first propositions are to be used in demonstrating. First, in affirmative demonstrations. Secondly, in negatives (85a3). In regard to the first he does three things. First, he shows how first and immediate propositions should be taken in demonstrations. Secondly, how such propositions are related to demonstrations (8038). Thirdly, he summarizes (85a2).
lib. 1 l. 36 n. 10 Dicit ergo primo, quod quando oportet demonstrare aliquam conclusionem affirmativam, puta, omne b est a, necesse est accipere aliquid quod primo praedicetur de b quam a, et de quo a etiam praedicetur, et sit illud c; et si iterum aliquid sit, de quo a per prius praedicetur quam de c, sic semper procedendo; sic nec propositio nec terminus significans aliquod ens accipietur in demonstrando extra ipsum a, quia oportebit quod a praedicetur de eo per se, et ita quod contineatur sub eo et non sit ab eo extrinsecum; sed oportebit semper condensare media. Et loquitur ad similitudinem hominum, qui videntur esse condensati sedentes in aliqua sede, quando inter sedentes nullus potest intercidere medius. Ita et media in demonstratione dicuntur densata, quando inter terminos acceptos nihil cadit medium. Et hoc est quod dicit, quod medium densatur quousque perveniatur ad hoc quod spatia fiant indivisibilia; idest, distantiae inter duos terminos sint tales, quod non possint dividi in plures huiusmodi distantias, sed sit unum spatium tantum. Et hoc contingit, quando propositio est immediata. Tunc enim vere est una propositio non solum actu, sed etiam potentia, quando est immediata. Si enim sit mediata, quamvis sit una in actu, quia unum praedicatur de uno, tamen est multa in potentia, quia accepto medio formantur duae propositiones. Sicut etiam linea, quae est una in actu in quantum est continua, est tamen multa in potentia, in quantum est divisibilis per punctum medium. Et ideo dicit quod propositio immediata est una sicut simplex indivisibilis.	He says therefore first (84b32) that when one is required to demonstrate an affirmative conclusion, for example, “Every B is A,” it is first necessary to take something which is first predicated of B before A is, and of which A is also predicated, say C. Furthermore, if there is something of which A is predicated before A is predicated of C, and something ahead of that, and so on, then no proposition and no term signifying a being outside of A will be taken in the demonstration, because it will be necessary that A be predicated of it per se in such a way that it is contained under it and is not extraneous to it; but it will always be necessary to condense (crowd together] the middles. (Here he is speaking according to an example of men who appear crowded together when they are sitting on a bench and there is no room for anyone else to sit between any two who are seated; in like fashion, the middles in demonstrations are condensed when no middle falls between the terms taken). And this is his meaning when he says, “the middle is condensed until the spaces become indivisible,” i.e., the distances between two terms are such that they cannot be divided into several such distances, but there is only one space. And this occurs when a proposition is immediate. For it is then that a proposition is one, not only actually but potentially, when it is immediate. For if it is mediate, then although it is actually one (because one thing is predicated of one thing), it is in fact several in potency, because when the middle is taken, two propositions are formed. In the same way, a line which is actually one, inasmuch as it is continuous, is several in potency, inasmuch as it is divisible at an intermediate point. Hence he says that an immediate proposition is one as a simple indivisible.
lib. 1 l. 36 n. 11 Deinde cum dicit: et quemadmodum in aliis etc., ostendit quomodo se habeat propositio immediata ad demonstrationem. Ubi considerandum est quod, sicut habetur in X Metaphys., in quolibet genere oportet esse unum primum, quod est simplicissimum in genere illo, et mensura omnium quae sunt illius generis. Et quia mensura est homogenea mensurato, secundum diversitatem generum oportet esse huiusmodi prima indivisibilia diversa. Unde hoc non est idem in omnibus: sed in gravitate ponderum accipitur ut unum indivisibile uncia, sive mna, idest quoddam minimum pondus; quod tamen non est simplex omnino, quia quodlibet pondus est divisibile in minora pondera, sed accipitur ut simplex per suppositionem. In melodiis autem accipitur ut unum principium tonus, qui consistit in sesquioctava proportione, vel diesis, quae est differentia toni et semitonii. Et in diversis generibus sunt diversa principia indivisibilia.	Then (8038) he shows the relation between an immediate proposition and a demonstration. Here we should note that, as it is stated in Metaphysics X, in every genus there must be one first thing which is the most simple in that genus and is the measure of all the things in that genus. And because a measure is homogeneous to the thing measured, such first indivisibles will vary according to the diversity of genera. Hence these will not be the same in all genera: but in regard to weights one indivisible, the ounce or mina, is taken as the minimum weight (even though it is not the absolute minimum, because every weight is further divisible into smaller weights, but it is taken as a minimum by supposition). Again, in melodies there is taken as the one principle “a tone,” which consists in a proportion of an octave and a half or a “diesis,” which is the difference between a tone and a semi-tone. Similarly, in diverse genera there are diverse indivisible principles.
Syllogismi autem principia sunt propositiones; unde oportet quod propositio simplicissima, quae est immediata, sit unum, quod est mensura syllogismorum. Demonstratio autem addit supra syllogismum quod facit scientiam. Comparatur autem intellectus ad scientiam sicut unum et indivisibile ad multa. Nam scientia est per decursum a principiis ad conclusiones; intellectus autem est absoluta et simplex acceptio principii per se noti. Unde intellectus respondet immediatae propositioni; scientia autem conclusioni, quae est propositio mediata. Sic igitur demonstrationis, in quantum est syllogismus, unum indivisibile est propositio immediata. Ex parte autem scientiae, quam causat, unum eius est intellectus.	Now the principles of a syllogism are propositions; hence it is required that the most simple proposition, which is immediate, be the unit which is the measure of syllogisms. But demonstration has, over and above a syllogism, the added feature that it causes science. Now “understanding” and science are related as the indivisible unit is related to the many. For science is effected by going from principles to conclusions, whereas “understanding” is the absolute and simple acceptance of a self-evident principle. Hence “understanding” corresponds to the immediate proposition, and science to a conclusion, which is a mediate proposition. Consequently, the indivisible unit of a demonstration regarded as a syllogism is the immediate proposition. But on the part of the science which it causes, the unit is “understanding.”
lib. 1 l. 36 n. 12 Deinde cum dicit: in demonstrativis quidem etc., epilogando concludit quod supra ostensum est, scilicet quod in affirmativis syllogismis medium non cadit extra extrema.	Then (85a2) he sums up and concludes what was established above, namely, that the middle in affirmative syllogisms does not fall outside the extremes.
lib. 1 l. 36 n. 13 Deinde cum dicit: in privativis autem ubi quidem etc., ostendit quomodo utendum sit propositionibus immediatis in syllogismis negativis. Et primo, in prima figura; secundo, in secunda; ibi: si vero oporteat monstrare etc.; tertio, in tertia; ibi: in tertio autem modo et cetera. Dicit ergo primo, quod in negativis syllogismis, nihil mediorum acceptorum procedendo ad immediata cadit extra genus terminorum affirmativae propositionis in prima figura: puta si demonstrandum sit quod nullum b est a, et accipiatur medium c, tali existente syllogismo, nullum c est a; omne b est c; ergo nullum b est a. Si ergo oporteat iterum probare quod in nullo c sit a, oportet accipere medium ipsius c et a, quod scilicet praedicetur de c, et per consequens de b, et sic pertinebit ad genus terminorum affirmativae propositionis: et ita semper procedetur quod media accepta non cadent extra affirmativam propositionem; cadent tamen extra genus praedicati negativi, puta extra genus a.	Then (850) he shows how to use immediate propositions in negative syllogisms. First, in the first figure. Secondly, in the second (85a7). Thirdly, in the third (8500). He says therefore first (85a3) that in negative syllogisms in the first figure, none of the middles taken while proceeding to immediates will fall outside the genus of the terms of an affirmative proposition; for example, if it is to be demonstrated that “No B is A,” and the middle taken is C, we have the following syllogism: “No C is A; but every B is C: therefore, No B is A.” Now if it should be necessary to prove that “No C is A,” one will be required to take a middle of C and A, i.e., one that will be predicated of C and consequently of B; thus it will belong to the genus of the terms of the affirmative proposition. And so it will always turn out that the middles taken will not fall outside the affirmative proposition, although they will fall outside the genus of the negative predicate, i.e., outside the genus of A.
lib. 1 l. 36 n. 14 Deinde cum dicit: si vero oporteat demonstrare etc., ostendit qualiter hoc se habeat in secunda figura; et dicit quod si oporteat demonstrare quod nullum e sit d, in secunda figura, accipiendo medium c, ut fiat talis syllogismus, omne d est c; nullum e est c, aut, quoddam e non est c; ergo nullum, vel, non omne e est d; nunquam medius terminus acceptus cadet extra e. Quia si oportebit iterum demonstrare quod nullum e est c, oportebit iterum accipere aliquod medium inter e et c; quia oportebit in secunda figura semper probare negativam; affirmativa enim in hac figura probari non potest. Unde sicut in prima figura media accepta semper accipiuntur ex parte propositionis affirmativae, ita oportet in secunda figura semper media accipi ex parte propositionis negativae.	Then (85a7) he shows how it is in the second figure, saying that if one is required to demonstrate in the second figure that “No E is D,” by taking C as middle, so as to form the syllogism, “Every D is C; but No E is C or Some E is not C: therefore, No E is D or Not every E is D,” the middle term taken will never fall outside of E. For if it should be necessary to demonstrate that “no E is C,” one will have to find a middle between E and C, because in the second figure it will always be necessary to prove a negative, since an affirmative cannot be concluded in this figure. Hence, just as in the first figure the middles are always taken on the side of the affirmative proposition, so in the second figure the middles will always be taken on the side of the negative proposition.
lib. 1 l. 36 n. 15 Deinde cum dicit: in tertio autem modo etc., ostendit qualiter hoc se habeat in tertia figura; et dicit quod in tertia figura media accepta non erunt neque extra praedicatum, quod negatur, neque extra subiectum, a quo negatur. Et hoc ideo quia medium subiicitur affirmativae vel negativae utrique; unde si oportet accipere adhuc aliquod medium, oportet iterum illud medium subiici utrique affirmando vel negando; et sic media accepta nunquam accipientur neque extra praedicatum negatum nec extra subiectum, de quo negatur.	Then (85a10) he shows how it is in the third figure, saying that in the third figure the middles which are taken will not be outside the predicate which is denied, nor outside the subject of which it is denied. The reason for this is that the middle is the subject in both propositions, whether affirmative or negative: hence if it is necessary to take yet another middle, it will again have to act as the subject of both, whether affirming or denying. And so the middles which are taken will never be taken outside the predicate which is denied, or outside the subject of which it is denied.

Notes

Latin	English
	English translation by Fabian R. Larcher, O.P.