Authors/Thomas Aquinas/metaphysics/liber11/lect13

Lecture 13

Latin	English
lib. 11 l. 13 n. 1 Notificat quae circumstant motum, et praecipue motum localem. Et primo notificat ea. Secundo inducit quaedam corollaria ex dictis, ibi, quare palam. Dicit ergo primo, quod simul secundum locum dicuntur quaecumque sunt in uno loco primo, idest proprio. Si enim aliqua sunt in uno loco communi, non propter hoc dicuntur esse simul: sic enim omnia, quae continentur caeli ambitu, dicerentur esse simul.	2404. He explains the terms which apply to motion, especially local motion. First (1021)C 2404), he explains them. Second (1022:C 2413), he draws a corollary from his remarks (“It is evident”). He accordingly says, first (1021), that things which are “in one primary place,” i e., a proper place, are said to be together in place; for if some things are in one common place, they are not for this reason said to be together, for then all things which are contained in the circumference of the heavens would be said to be together.
lib. 11 l. 13 n. 2 Seorsum autem dicuntur quaecumque sunt in alio et alio loco.	2405. Things which are in different places are said to be separate.
lib. 11 l. 13 n. 3 Tangi autem adinvicem dicuntur, quorum ultima sunt simul; puta duo corpora quorum superficies coniunguntur.	2406. And those whose extremities are said to touch one another are said to be in contact; for example, two bodies whose surfaces are joined.
lib. 11 l. 13 n. 4 Medium autem inter duo est, in quod id quod continuo permutatur, natum est prius pervenire quam in ultimum. Sicut si motus continuus de a in c, prius veniet in b, id quod mutatur, quam in c.	2407. And an intermediate between two things is that at which it is natural for something that continuously changes to arrive before it reaches its limit; for example, if there is continuous motion from a to c, the thing being changed first arrives at b before it reaches c.
lib. 11 l. 13 n. 5 Contrarium vero secundum locum est, quod est plurimum distans secundum rectam lineam. Non enim distantia plurima potest mensurari secundum lineam curvam, eo quod inter duo puncta possunt designari infinitae decisiones circulorum dissimiles. Sed inter duo puncta non potest esse nisi una linea recta. Mensuram autem oportet esse certam et determinatam. Plurimum autem distans in locis invenitur secundum naturam sursum et deorsum, quae sunt medium et extremum mundi.	2408. Again, that which is most distant in a straight line is contrary in place; for that which is most distant cannot be measured by a curved line, because an infinite number of unlike sections of circles can be drawn between two points, but there can be only one straight line between two points. Now a measure must be definite and fixed. And that which is most distant as to place admits of being above and below, which are the extremity and the center of the universe.
lib. 11 l. 13 n. 6 Consequenter autem dicitur quod est post aliquod primum principium; sive attendatur ordo secundum positionem, sive secundum speciem, sicut binarius est post unitatem, sive qualitercumque aliter. Adhuc autem oportet quod nihil eiusdem generis sit medium inter id quod est consequenter et id cui consequenter est. Sicut lineae sunt consequenter alicui lineae, et unitates alicui unitati, et domus alicui domui consequenter. Sed nihil prohibet inter duo, quorum unum se habet consequenter ad alterum, esse aliquid medium alterius generis; puta si inter duas domus sit unus equus medius. Et ad manifestandum praemissam divisionem subiungit, quod illud quod dicitur consequenter, oportet quod sit consequenter respectu alicuius, et quod sit aliquod posterius. Unum enim non se habet consequenter ad duo, cum sit prius, neque nova luna ad secundam, sed e converso.	2409. That is said to be subsequent which comes after some starting point, whether the order is determined by position or by form or in some other way; for example, two comes after one. And there must also be nothing of the same genus between that which is subsequent and that which it follows, as lines are subsequent to a line and units to a unit and a house to a house. But nothing prevents something of another genus from being an intermediate between two things one of which follows the other; for example, there may be one intermediate horse between two houses. In order to make the above distinction clear he adds that what is said to follow something must be subsequent and come after something. For one does not come after two, since it is first; nor does the first day of the new moon follow the second, but the other way around.
lib. 11 l. 13 n. 7 Deinde dicit quod habitum dicitur illud quod est consequenter et tangit; puta si duo corpora sint ordinata, quorum unum alterum tangat.	2410. Then he says that the contiguous means what is subsequent and in contact with something else-for example, if two bodies are so related that one touches the other.
lib. 11 l. 13 n. 8 Deinde dicit quod, cum omnis permutatio sit inter opposita, et opposita inter quae est permutatio sint contraria et contradictoria, ut ostensum est; et cum contradictionis nullum sit medium: manifestum est quod inter sola contraria oportet esse medium, cum medium sit inter extrema motus, ut ex definitione superius posita patet. Hoc autem bene inducit. Quia enim dixerat quod consequenter sunt, inter quae non est medium, conveniens fuit ut ostenderetur inter quae potest esse medium.	2411. Then he says that, since every change is between opposites, and the opposites between which there is change are either contraries or contradictories, as has been shown (1008:C 2363), and since there is no intermediate between contradictories, it is evident that there is an intermediate only between contraries; for that which is intermediate is between the limits of a motion, as is clear from the definition given above. His introduction of this is timely; for since he said that those things are subsequent between which there is no intermediate, it was fitting that he should indicate between what things it is possible to have an intermediate.
lib. 11 l. 13 n. 9 Deinde ostendit quid sit continuum: et dicit, quod continuum addit aliquid supra habitum. Et dicit quod continuum est cum utriusque eorum, quae se tangunt, et quae simul sunt, sit unus et idem terminus, sicut partes lineae continuantur ad punctum.	2412. Then he shows what the continuous is. He says that the continuous adds something to the contiguous; for there is continuity when both of those things which are in contact and together have one and the same extremity, as the parts of a line are continuous in relation to a point.
lib. 11 l. 13 n. 10 Deinde cum dicit quare palam inducit tria corollaria ex praemissis. Quorum primum est, quod continuum est in illis ex quibus natum est fieri unum secundum contactum. Et hoc ideo est, quia continuum requirit identitatem termini.	2413. It is evident (1022). Then he draws three corollaries from what has been said. The first is that continuity belongs to those things from which one thing naturally results in virtue of their contact; and this is because the continuous requires identical extremities.
lib. 11 l. 13 n. 11 Secundum corollarium est, quod inter ista tria, consequenter, contactum et continuum, prius et communius est quod est consequenter. Non enim omne quod est consequenter tangit, sed omne quod tangit est consequenter. Oportet enim contacta secundum positionem esse ordinata, et nihil eorum esse medium. Et similiter tangens est prius et communius ens quod continuum; quia si est continuum, est necesse quod tangat. Quod enim est unum, necesse est esse simul; nisi forte intelligatur in hoc, quod est esse simul, pluralitas. Sic enim continuum non esset contactum. Sed eo modo quo id quod est unum est simul, necesse est continuum esse tangens. Sed non sequitur, si tangit, quod sit continuum; sicut non sequitur quod si aliqua sunt simul, quod sint unum. Sed in quibus non est contactus non est nascentia, idest naturalis coniunctio, quae est proprie continuorum.	2414. The second corollary is that, of these three things—the subsequent, the contiguous and the continuous—the first and most common is the subsequent; for not everything that is subsequent is in contact, but everything which is in contact is subsequent or consecutive. For things which are in contact are arranged according to their position, and no one of them is an intermediate. Similarly, the contiguous is prior to and more common than the continuous, because, if a thing is continuous, there must be contact. For what is one must be together, unless perhaps plurality is understood in the phrase being together. For in that case the continuous would not involve being in contact. But the continuous must involve contact in the way in which something one is together. Yet if there is contact it does not follow that there is continuity; for example, if certain things are together it does not follow that they are one. But in things in which there is no contact “there is no natural coherence,” i.e., natural union, which is a property of the continuous.
lib. 11 l. 13 n. 12 Tertium corollarium est, quod punctus et unitas non sunt idem, ut Platonici posuerunt, dicentes quod punctum est unitas habens positionem. Et quod non sint idem, patet ex duobus. Primo quidem, quia secundum puncta est contactus, non autem secundum unitates, sed consequenter se habent adinvicem. Secundo, quia inter duo puncta semper est aliquid medium, ut probatur in sexto physicorum. Sed inter duas unitates necesse non est aliquid esse medium.	2415. The third corollary is that the point and the unit are not the same, as the Platonists claimed when they said that the point is the unit having position. That they are not the same is evident for two reasons: first, because there is contact between points but not between units, which only follow each other; second, because there is always some intermediate between two points, as is proved in Book V of the Physics. But it is not necessary that there should be an intermediate between two units.