Authors/Thomas Aquinas/physics/L8/lect22

Lecture 22 Diversity of movers annuls continuity of motion

Latin	English
	Lecture 22 Diversity of movers annuls continuity of motion
lib. 8 l. 22 n. 1 Postquam philosophus ostendit duo quae sunt necessaria ad principale propositum ostendendum, scilicet quod potentia finita non possit movere tempore infinito, et quod potentia infinita non possit esse in magnitudine finita; nunc accedit ad probandum tertium, scilicet unitatem primi motoris. Et circa hoc duo facit: primo enim ostendit quod propter diversitatem motorum, deficit continuitas vel unitas motus, in quibusdam mobilibus quae videntur continue moveri; secundo ostendit ex hoc quod primum motorem necesse est esse unum, ibi: quoniam autem in his et cetera. Circa primum tria facit: primo enim movet dubitationem de his quae proiiciuntur; secundo solvit dubitationem, ibi: necesse autem etc.; tertio ostendit ex hoc quod motus corporis proiecti non est continuus, ibi: hic quidem igitur et cetera. Circa primum duo facit: primo ponit dubitationem; secundo excludit quandam solutionem, ibi: si autem simul et cetera. Proponit ergo dubitationem primo de his quae feruntur proiecta: quae talis est. Ostensum est supra in principio huius octavi, quod omne quod movetur, ab alio movetur, dummodo non sit de illis quae movent seipsa, sicut sunt animalia; de quorum numero non est lapis proiectus. Movet autem corporale per contactum. Est ergo dubitatio quomodo proiecta continue moventur, etiam postquam non tanguntur a movente. Videtur enim quod moveantur, nullo movente ipsa.	1160. After proving two of the things needed for demonstrating his proposition, namely, that a finite power cannot move in an infinite time, and that an infinite power cannot exist in a finite magnitude, the Philosopher now starts to prove the third, namely, the unity of the first mover. About this he does two things: First he shows that on account of the diversity of movers, the continuity or unity of motion fails in certain mobiles that seem to be in continuous motion; Secondly, he shows from this that the first mover is necessarily one, (L. 23). About the first he does three things: First he raises a doubt about projectiles; Secondly, he resolves the doubt, at 1162; Thirdly, from this he shows that the motion of a projectile is not continuous, at 1163. About the first he does two things: First he states the doubt; Secondly, he rejects one solution, at 1161. He proposes therefore First (909 266 b30) a doubt about projectiles. It is this: It was proved above in the beginning of this Book that whatever is being moved is being moved by another, provided we are not referring to things that move themselves, such as animals, of which a projected stone is not one. Now a bodily thing causes motion through contact. Therefore there is doubt as to how projectiles remain in continuous motion even after contact with the mover ceases. For they seem to be moved without anything moving them.
lib. 8 l. 22 n. 2 Deinde cum dicit: si autem simul movet etc., excludit quandam solutionem, quae dicitur fuisse Platonis, qui dicebat quod proiiciens qui primo movit lapidem, simul etiam cum lapide movit aliquid aliud, scilicet aerem, et aer motus movet lapidem etiam post contactum proiectoris. Sed hanc solutionem excludit: quia similiter videtur impossibile quod moveatur aer non tangente neque movente primo, scilicet proiectore, sicut erat impossibile de lapide; sed videtur esse necessarium quod simul dum primum movens movet, omnia moveantur, et dum primum movens quiescit, idest cessat a movendo, omnia quiescant; quamvis etiam aliquid motum a primo movente, sicut lapis, faciat aliquid moveri, sicut id quod primo movit movebat.	1161. Then at (909 266 b30) he rejects a solution attributed to Plato who said that the projector who first moves a stone moves not only the stone but something else, namely, the air, and the moved air moves the stone, even after contact by the projector. But he rejects this solution, on the ground that it appears equally as impossible for the air to be moved when the first mover, namely, the projector, is no longer in contact with it, nor moving it, as it was for the stone. But rather it seems to be necessary that while the first mover is acting, all are being moved, and when the first mover rests, i.e., ceases to act, all rest, although also something moved by the first mover, such as the stone, may cause something to be moved, just as the original mover did.
lib. 8 l. 22 n. 3 Deinde cum dicit: necesse autem hoc quidem dicere etc., ponit suam solutionem. Et dicit quod si secundum movens movet motum a primo movente, necesse est hoc dicere, quod primum movens, scilicet proiiciens, det secundo moventi, scilicet aeri vel aquae vel cuicumque tali corpori quod est natum movere corpus proiectum, ut possit movere et ut possit moveri: utrumque enim habet aer vel aqua a proiiciente, et quod moveat et quod moveatur. Sed quia movere et moveri non de necessitate sunt in eodem, cum inveniatur aliquod movens non motum; non simul pausat movens et quod movetur, idest aer motus a proiiciente non simul cessat movere et moveri; sed statim cum primum movens, idest proiiciens, cessaverit movere, et aer cessat moveri, sed adhuc movet. Et hoc manifestum est ad sensum: quia quando aliquod mobile iam pervenerit ad terminum motus, in ipso ultimo perventionis potest movere; sed tunc non movetur, sed est in motum esse. Dum autem secundum movens movet, movetur illud quod est habitum, idest consequenter se habens ad ipsum. Et de hoc etiam tertio est eadem ratio, quia remanet movens etiam quando non movetur. Et quia secundum movens habet minus de potentia movendi quam primum, et tertium quam secundum, oportet quod cesset motus proiectionis; ex hoc scilicet quod minor est virtus movendi in habito, idest in consequenti, quam in eo in quo primo fuit. Et sic tandem, propter minorationem virtutis movendi, venietur ad hoc quod id quod erit prius respectu sui consequentis, non faciet ipsum consequens habere potentiam movendi, sed faciet ipsum tantummodo moveri. Et tunc necesse est quod simul dum hoc ultimum movens pausat a movendo, et motum ab ipso pausabit a moveri; et per consequens pausabit totus motus, quia ultimum motum non potest movere aliquid aliud.	1162. Then at (910 267 a2) he gives his own solution. And he says that if the second mover causes motion insofar as it is moved by the first mover, then it is necessary to say that the first mover, namely, the thrower, gives to the second mover, namely, the air or water or any such body apt to move a thrown body, the ability both to cause motion and to be moved; for both of these are received into the air or water from the thrower, namely, to cause motion and to be moved. But since to cause motion, and to be moved, are not of necessity in the same thing—since there is found a mover that is not itself moved —the mover and moved do not pause simultaneously, i.e., the air moved by the thrower does not simultaneously cease causing motion and cease being moved, but as soon as the thrower ceases acting, the air ceases to be moved, but still moves. And this is evident to the senses. For when a mobile has now arrived at the terminus of its motion, it is able to cause motion in the ultimate moment of its arrival, at which time it is no longer being moved but is in the state of having been moved. Now while the second mover moves, that which is “had,” i.e., which is next to it, is being moved. And the same applies to this third, for it remains a mover even when it is not being moved. And because a second mover has less power for acting than did the first, and the third less than the second, the motion called “projection” must cease, on account of the fact, namely, that the power for moving is less in the “had,” i.e., the subsequent, mover than in that in which it was first. Thus at length, on account of the diminution of the power to move, a state is reached where that which was prior with respect to the one following will not confer upon the one following the power to cause motion but will solely cause it to be moved. And at that time it is necessary that when this last mover ceases to act upon the one following it, simultaneously that moved by it will cease being moved, Consequently, the entire motion will cease, because the last moved object is unable to cause motion in any other.
lib. 8 l. 22 n. 4 Deinde cum dicit: hic quidem igitur etc., concludit ex praemissis quod iste motus proiectionis non sit continuus. Dicit ergo quod hic motus, scilicet proiectionis, fit in corporibus quae contingit aliquando moveri et aliquando quiescere, si qua vere sunt quibus conveniat. Quod patet ex dictis: quiescit enim proiectionis motus per defectum virtutis movendi, ut dictum est. Patet etiam ex praemissis quod iste motus non est continuus, etsi continuus videatur. Videtur enim continuus propter mobilis unitatem: non tamen est continuus, quia sunt diversa moventia, ut dictum est. Aut enim iste motus est a pluribus moventibus consequenter se habentibus, aut etiam a pluribus moventibus se tangentibus (quomodo autem differant consequenter se habere et tangere, supra dictum est in quinto et sexto). Et manifestum est ad sensum, quod utroque modo se habentibus diversis moventibus, possunt movere unum mobile, secundum quod ipsa moventur ab aliquo primo movente. In his enim quae moventur motu proiectionis, non est unum movens tantum, sed multa habita ad invicem, et consequenter se habentia et contacta. Et quia diversitas non est absque divisione, ideo praedictus proiectionis motus fit per medium facile divisibile, scilicet per aerem et aquam, in quibus propter divisionem de facili contingit diversitas moventium. Quem quidem motum proiectionis aliqui dicunt esse antiperistasim, idest contra-resistentiam; ex eo scilicet quod aer circumstans motus, aliquo modo movet corpus proiectum, sicut supra dictum est in quarto. Sed non potest praedicta dubitatio solvi nisi eo modo qui positus est: quia si ponatur causa proiectionis antiperistasis aeris, sequitur quod omnia simul moveant et moveantur, idest quod totus aer simul moveat et moveatur, et per consequens quod simul quiescant omnia; quod patet esse falsum. Videmus enim unum aliquid esse quod continue movetur, a quocumque moveatur. Quod ideo dico, quia non habet unum et idem determinatum movens, sed moventia diversa.	1163. Then at (911 267 a12) he concludes from the foregoing that a motion of projection is not continuous. He says, therefore, that this motion, namely, that of projection, comes to be in bodies that are capable of being moved at one time and of resting at another time—if indeed there are bodies to which such a motion belongs. And this is evident from what was said; for the motion called “projection” ceases through a failing of the power to cause motion, as has been said. It is also evident from the foregoing that this motion is not continuous, although it appears to be continuous. For it seems to be continuous, because there is one mobile involved; yet it is not continuous, because there are diverse movers, as has been said. For either that motion results from a series of consecutive movers or from a series of movers that are in contact—(how “consecutive” and “in contact” differ has been explained above in Books V and VI). And it is plain to sense that in both cases the different movers can move one mobile inasmuch as they are moved by some first mover. For in things that are moved in a way that projectiles are moved, there is not just one mover but many “had” to each other (i.e., following each other), which are consecutive and in contact. And because diversity is not without division, the projection in question comes to be through a medium that is easy to divided namely, air and water, in which a diversity of movers can function on account of the easy divisibility of the medium. This motion of projection is by some called antiperistasistasis, i.e., contra-resistance, on the ground that the surrounding air being set in motion somehow moves the projectile, as was said in Book IV. However, the problem under discussion can be solved in no other way than the way mentioned. Because, if the contra-resistance of the air is the cause of the projection, it follows that all the elements involved are moving and being moved simultaneously, i.e., that the entire air is simultaneously acting and being acted upon and, consequently, that all would cease simultaneously. But this is evidently false, For we see some one thing being moved continuously no matter what moves it. And I say this because it does not have one and the same determinate mover, but diverse movers.