Volume 1 · p. 202
End of Chapter IV and Chapter V. How place is continuous quantity
tempus est numerus, non intelligitur quod secundum unum et idem sit continuum et numerus: secundum enim quod adjacet protensioni ejus quod movetur est continuum, secundum autem quod instanti copulante distinguitur id quod est ante ab eo quod est post, et iteratur hoc in toto motu, sic est numerus. Et quando dicitur quod est numerus, non dicitur nec intelligitur quod simpliciter sit numerus, sed quod est numerus motus per esse motus: sed motus per prius et posterius, quod iteratur in motu sicut id quod movetur in toto spatio motus. Propter quod non sequitur quod tempus sit simpliciter continua quantitas. Et ideo manifestum est quod non est in duobus generibus primis quantitatis ex æquo, scilicet in genere continui et in genere discreti, sed simpliciter est in genere continui et secundum aliquid accipit formam discreti. Patet etiam qualiter fluit tempus ab hoc indivisibili quod est instans.
Sed remanet quæstio, quare motus non ponatur esse in genere quantitatis sicut tempus? præcipue cum multis rationibus probet Aristoteles 1 motum esse divisibilem in infinitum, et cum expresse dicat motum esse speciem quantitatis in quinto primæ philosophiæ 2. Sed ad hoc per ante dicta facilis est responsio: si enim consideretur id quod dat motui speciem et nomen, et per consequens dat ei genus, eo quod species et genus ad unam pertinent naturam: tunc videbitur causa ejus quod quæritur: quale enim dat alterationi nomen et speciem, propter quod dicitur in genere alteratio, et secundum speciem calefactio, vel albatio. Et sic similiter est ubi quod motui locali dat nomen et speciem et genus. Et similiter in augmentatione. Et facile est videre in omnibus aliis sicut motus per accidens qui in omnibus est generibus. Continuitas autem motus non est a natura illa quæ fluit, sed potius est causata a processione illius in quo est motus ut in subjecto: subjectum autem non est aliquid de essentia illius quod est in ipso, et ideo motus proprium et sibi determinatum genus non habet. Alia autem quæ dicenda erant de tempore, vel ad physicum pertinent, vel ad metaphysicum, et ideo illuc differantur: in quarto enim Physicorum 3 determinabitur natura temporis: in parte autem illa primæ philosophiæ quæ est de causis determinabitur qualiter tempus se habet ad æternitatem, et qualiter se habet nunc temporis ad nunc æternitatis. Quantum autem pertinet ad intentionem logicam de tempore sufficere videtur quod modo dictum est.
CAPUT V.
Qualiter locus est quantitas continua.
Nunc autem videndum est qualiter locus est continua quantitas. Locus est quidem ubi continentur corporis locati particulæ, qui locus distantia est in qua distenditur tota corporis quantitas, ita quod nihil corporis vel partium corporis est extra illam distantiam secundum longum, latum et profundum corporis: est enim tanta illa distantia, quantum est corpus, et nec minor nec major, sed in toto est corpore commensurata: sicut distantia diametrorum corporum quæ sit protensa inter spatium diametrorum loci et corporis, secundum esse quidem est una et eadem, ut probatur, distantiæ locali. Et hæc quidem distantia loci et corporis secundum esse quidem est una et eadem, ut probat Aristoteles 4 contra Philosophum loquens qui Xutos vocatur. Quamvis autem secundum esse sit eadem, differt tamen superficiebus continentibus, et differt actu mensuræ et ratione mensurandi. Superficie quidem: quia loci superficies est extra locatum, et continens et tangens undique locatum. Superficies
time is a number, it is not understood that according to one and the same thing it is continuous and a number; for according as it lies adjacent to the stretching-out of that which is moved, it is continuous, but according as, with the instant joining, that which is before is distinguished from that which is after, and this is repeated in the whole motion, thus it is a number. And when it is said that it is a number, it is not said or understood that it is simply a number, but that it is the number of motion through the being of motion; but of motion through prior and posterior, which is repeated in motion as that which is moved is repeated in the whole space of motion. On account of this it does not follow that time is simply a continuous quantity. And therefore it is manifest that it is not in the two first genera of quantity equally, namely in the genus of the continuous and in the genus of the discrete, but simply it is in the genus of the continuous and according to something receives the form of the discrete. It is also clear how time flows from this indivisible which is the instant.
But the question remains why motion is not posited to be in the genus of quantity as time is, especially since Aristotle proves by many arguments 1 that motion is divisible to infinity, and since he expressly says that motion is a species of quantity in the fifth book of First Philosophy 2. But to this, through the things said before, the response is easy: for if that which gives species and name to motion is considered, and consequently gives it genus, because species and genus pertain to one nature, then the cause of what is asked will be seen. For quality gives name and species to alteration, on account of which alteration is said in the genus, and heating or whitening according to species. And similarly in this way where gives name and species and genus to local motion. And similarly in increase. And it is easy to see in all the others, as accidental motion, which is in all genera. But the continuity of motion is not from that nature which flows, but rather is caused by the procession of that in which motion is as in a subject; but the subject is not something of the essence of that which is in it, and therefore motion does not have its own genus determined for itself. But the other things which had to be said about time pertain either to the physicist or to the metaphysician, and therefore they are deferred to that place: for in the fourth book of the Physics 3 the nature of time will be determined; but in that part of First Philosophy which is concerning causes it will be determined how time is related to eternity, and how the now of time is related to the now of eternity. But as much as pertains to the logical intention concerning time, what has now been said seems to suffice.
CHAPTER V.
How place is continuous quantity.
But now it must be seen how place is continuous quantity. Place is indeed where the parts of the located body are contained, which place is the distance in which the whole quantity of the body is stretched out, so that nothing of the body or of the parts of the body is outside that distance according to the length, breadth, and depth of the body. For that distance is as great as the body is, and neither smaller nor larger, but is commensurated with the body in the whole, just as the distance of the diameters of bodies, which is stretched between the space of the diameters of place and of body, according to being indeed is one and the same, as is proved, with local distance. And this distance of place and of body according to being indeed is one and the same, as Aristotle proves 4 against the speaker Philosopher who is called Xutos. But although according to being it is the same, nevertheless it differs by the containing surfaces, and it differs by the act of measure and by the account of measuring. By surface indeed: because the surface of place is outside the located thing, and containing and touching the located thing on every side. The surface
Notes
- Aristotle, in book 8 of the Physics, text, commentary 33. (Aristoteles, In 8 Physic. tex. com. 33.) ↩
- The same, in book 5 of First Philosophy, from text, commentary 18. (Id. In 5 primæ philosophiæ, a tex. com. 18.) ↩
- The same, in book 4 of the Physics, from text, commentary 87 up to the end. (Id. In 4 Physic. a tex. com. 87 usque in finem.) ↩
- Aristotle, in book 4 of the Physics, from text, commentary 79. (Aristoteles, In 4 Physicorum, a tex. com. 79.) ↩
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