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BOOK V

Lectio 1 Per se notion is distinguished from per accidens
Chapter
Μεταβάλλει δὲ τὸ μεταβάλλον πᾶν τὸ μὲν κατὰ συμβεβηκός, οἷον ὅταν λέγωμεν τὸ μουσικὸν βαδίζειν, ὅτι ᾧ συμβέβηκεν μουσικῷ εἶναι, τοῦτο βαδίζει· τὸ δὲ τῷ τούτου τι μεταβάλλειν ἁπλῶς λέγεται μεταβάλλειν, οἷον ὅσα λέγεται κατὰ μέρη (ὑγιάζεται γὰρ τὸ σῶμα, ὅτι ὁ ὀφθαλμὸς ἢ ὁ θώραξ, ταῦτα δὲ μέρη τοῦ ὅλου σώματος)· ἔστι δέ τι ὃ οὔτε κατὰ συμβεβηκὸς κινεῖται οὔτε τῷ ἄλλο τι τῶν αὐτοῦ, ἀλλὰ τῷ αὐτὸ κινεῖσθαι πρῶτον. καὶ τοῦτ' ἔστι τὸ καθ' αὑτὸ κινητόν, κατ' ἄλλην δὲ κίνησιν ἕτερον, οἷον ἀλλοιωτόν, καὶ ἀλλοιώσεως ὑγιαντὸν ἢ θερμαντὸν ἕτερον.	Everything which changes does so in one of three senses. It may change (1) accidentally, as for instance when we say that something musical walks, that which walks being something in which aptitude for music is an accident. Again (2) a thing is said without qualification to change because something belonging to it changes, i.e. in statements which refer to part of the thing in question: thus the body is restored to health because the eye or the chest, that is to say a part of the whole body, is restored to health. And above all there is (3) the case of a thing which is in motion neither accidentally nor in respect of something else belonging to it, but in virtue of being itself directly in motion. Here we have a thing which is essentially movable: and that which is so is a different thing according to the particular variety of motion: for instance it may be a thing capable of alteration: and within the sphere of alteration it is again a different thing according as it is capable of being restored to health or capable of being heated.
ἔστι δὲ καὶ ἐπὶ τοῦ κινοῦντος ὡσαύτως· τὸ μὲν γὰρ κατὰ συμβεβηκὸς κινεῖ, τὸ δὲ κατὰ μέρος τῷ τῶν τούτου τι, τὸ δὲ καθ' αὑτὸ πρῶτον, οἷον ὁ μὲν ἰατρὸς ἰᾶται, ἡ δὲ χεὶρ πλήττει.	And there are the same distinctions in the case of the mover: (1) one thing causes motion accidentally, (2) another partially (because something belonging to it causes motion), (3) another of itself directly, as, for instance, the physician heals, the hand strikes.
ἐπεὶ δ' ἔστι μέν τι τὸ κινοῦν πρῶτον, ἔστι δέ τι τὸ κινούμενον, ἔτι ἐν ᾧ, ὁ χρόνος, καὶ παρὰ ταῦτα ἐξ οὗ καὶ εἰς (224b.) ὅ—πᾶσα γὰρ κίνησις ἔκ τινος καὶ εἴς τι·	We have, then, the following factors: (a) on the one hand that which directly causes motion, and (b) on the other hand that which is in motion: further, we have (c) that in which motion takes place, namely time, and (distinct from these three, d) that from which and (e) that to which it proceeds: for every motion proceeds from something and to something,
ἕτερον γὰρ τὸ πρῶτον κινούμενον καὶ εἰς ὃ κινεῖται καὶ ἐξ οὗ, οἷον τὸ ξύλον καὶ τὸ θερμὸν καὶ τὸ ψυχρόν· τούτων δὲ τὸ μὲν ὅ, τὸ δ' εἰς ὅ, τὸ δ' ἐξ οὗ—ἡ δὴ κίνησις δῆλον ὅτι ἐν τῷ ξύλῳ, οὐκ ἐν τῷ εἴδει· οὔτε γὰρ κινεῖ οὔτε κινεῖται τὸ εἶδος ἢ ὁ τόπος ἢ τὸ τοσόνδε, ἀλλ' ἔστι κινοῦν καὶ κινούμενον καὶ εἰς ὃ κινεῖται.	that which is directly in motion being distinct from that to which it is in motion and that from which it is in motion: for instance, we may take the three things 'wood', 'hot', and 'cold', of which the first is that which is in motion, the second is that to which the motion proceeds, and the third is that from which it proceeds. This being so, it is clear that the motion is in the wood, not in its form: for the motion is neither caused nor experienced by the form or the place or the quantity. So we are left with a mover, a moved, and a goal of motion.
μᾶλλον γὰρ εἰς ὃ ἢ ἐξ οὗ κινεῖται ὀνομάζεται ἡ μεταβολή. διὸ καὶ ἡ φθορὰ εἰς τὸ μὴ ὂν μεταβολή ἐστιν· καίτοι καὶ ἐξ ὄντος μεταβάλλει τὸ φθειρόμενον· καὶ ἡ γένεσις εἰς ὄν, καίτοι καὶ ἐκ μὴ ὄντος.	I do not include the starting-point of motion: for it is the goal rather than the starting-point of motion that gives its name to a particular process of change. Thus 'perishing' is change to not-being, though it is also true that that that which perishes changes from being: and 'becoming' is change to being, though it is also change from not-being.
τί μὲν οὖν ἐστιν ἡ κίνησις, εἴρηται πρότερον· τὰ δὲ εἴδη καὶ τὰ πάθη καὶ ὁ τόπος, εἰς ἃ κινοῦνται τὰ κινούμενα, ἀκίνητά ἐστιν, οἷον ἡ ἐπιστήμη καὶ ἡ θερμότης.	Now a definition of motion has been given above, from which it will be seen that every goal of motion, whether it be a form, an affection, or a place, is immovable, as, for instance, knowledge and heat.
καίτοι ἀπορήσειεν ἄν τις, εἰ τὰ πάθη κινήσεις, ἡ δὲ λευκότης πάθος·	Here, however, a difficulty may be raised. Affections, it may be said, are motions, and whiteness is an affection:
ἔσται γὰρ εἰς κίνησιν μεταβολή. ἀλλ' ἴσως οὐχ ἡ λευκότης κίνησις, ἀλλ' ἡ λεύκαν σις.	thus there may be change to a motion. To this we may reply that it is not whiteness but whitening that is a motion.
ἔστιν δὲ καὶ ἐν ἐκείνοις καὶ τὸ κατὰ συμβεβηκὸς καὶ τὸ κατὰ μέρος καὶ [τὸ] κατ' ἄλλο καὶ τὸ πρώτως καὶ μὴ κατ' ἄλλο, οἷον τὸ λευκαινόμενον εἰς μὲν τὸ νοούμενον μεταβάλλει κατὰ συμβεβηκός (τῷ γὰρ χρώματι συμβέβηκε νοεῖσθαι), εἰς δὲ χρῶμα ὅτι μέρος τὸ λευκὸν τοῦ χρώμα τος (καὶ εἰς τὴν Εὐρώπην ὅτι μέρος αἱ Ἀθῆναι τῆς Εὐρώπης), εἰς δὲ τὸ λευκὸν χρῶμα καθ' αὑτό.	Here also the same distinctions are to be observed: a goal of motion may be so accidentally, or partially and with reference to something other than itself, or directly and with no reference to anything else: for instance, a thing which is becoming white changes accidentally to an object of thought, the colour being only accidentally the object of thought; it changes to colour, because white is a part of colour, or to Europe, because Athens is a part of Europe; but it changes essentially to white colour.
πῶς μὲν οὖν καθ' αὑτὸ κινεῖται καὶ πῶς κατὰ συμβεβηκός, καὶ πῶς κατ' ἄλλο τι καὶ πῶς τῷ αὐτὸ πρῶτον, καὶ ἐπὶ κινοῦντος καὶ ἐπὶ κινουμένου, δῆλον, καὶ ὅτι ἡ κίνησις οὐκ ἐν τῷ εἴδει ἀλλ' ἐν τῷ κινουμένῳ καὶ κινητῷ κατ' ἐνέργειαν.	It is now clear in what sense a thing is in motion essentially, accidentally, or in respect of something other than itself, and in what sense the phrase 'itself directly' is used in the case both of the mover and of the moved: and it is also clear that the motion is not in the form but in that which is in motion, that is to say 'the movable in activity'.
ἡ μὲν οὖν κατὰ συμβεβηκὸς μεταβολὴ ἀφείσθω· ἐν ἅπασί τε γάρ ἐστι καὶ αἰεὶ καὶ πάντων· ἡ δὲ μὴ κατὰ συμβεβηκὸς οὐκ ἐν ἅπασιν, ἀλλ' ἐν τοῖς ἐναντίοις καὶ τοῖς μεταξὺ καὶ ἐν ἀντιφάσει· τούτου δὲ πίστις ἐκ τῆς ἐπαγωγῆς.	Now accidental change we may leave out of account: for it is to be found in everything, at any time, and in any respect. Change which is not accidental on the other hand is not to be found in everything, but only in contraries, in things intermediate contraries, and in contradictories, as may be proved by induction.
ἐκ δὲ τοῦ μεταξὺ μετα βάλλει· χρῆται γὰρ αὐτῷ ὡς ἐναντίῳ ὄντι πρὸς ἑκάτερον· ἔστι γάρ πως τὸ μεταξὺ τὰ ἄκρα. διὸ καὶ τοῦτο πρὸς ἐκεῖνα κἀκεῖνα πρὸς τοῦτο λέγεταί πως ἐναντία, οἷον ἡ μέση ὀξεῖα πρὸς τὴν ὑπάτην καὶ βαρεῖα πρὸς τὴν νητήν, καὶ τὸ φαιὸν λευκὸν πρὸς τὸ μέλαν καὶ μέλαν πρὸς τὸ λευκόν.	An intermediate may be a starting-point of change, since for the purposes of the change it serves as contrary to either of two contraries: for the intermediate is in a sense the extremes. Hence we speak of the intermediate as in a sense a contrary relatively to the extremes and of either extreme as a contrary relatively to the intermediate: for instance, the central note is low relatively—to the highest and high relatively to the lowest, and grey is light relatively to black and dark relatively to white.

Lectio 2
The species of change; which one is motion

Chapter 1 cont.
ἐπεὶ δὲ (225a.) πᾶσα μεταβολή ἐστιν ἔκ τινος εἴς τι (δηλοῖ δὲ καὶ τοὔνομα· μετ' ἄλλο γάρ τι καὶ τὸ μὲν πρότερον δηλοῖ, τὸ δ' ὕστερον), μεταβάλλοι ἂν τὸ μεταβάλλον τετραχῶς· ἢ γὰρ ἐξ ὑποκειμένου εἰς ὑποκείμενον, ἢ ἐξ ὑποκειμένου εἰς μὴ ὑποκείμενον, ἢ οὐκ ἐξ ὑποκειμένου εἰς ὑποκείμενον, ἢ οὐκ ἐξ ὑποκειμένου εἰς μὴ ὑποκείμενον· λέγω δὲ ὑποκείμενον τὸ καταφάσει δηλούμενον.	And since every change is from something to something—as the word itself (metabole) indicates, implying something 'after' (meta) something else, that is to say something earlier and something later—that which changes must change in one of four ways: from subject to subject, from subject to nonsubject, from non-subject to subject, or from non-subject to non-subject, where by 'subject' I mean what is affirmatively expressed.
ὕστε ἀνάγκη ἐκ τῶν εἰρημένων τρεῖς εἶναι μεταβολάς, τήν τε ἐξ ὑποκειμένου εἰς ὑποκείμενον, καὶ τὴν ἐξ ὑποκειμένου εἰς μὴ ὑποκείμενον, καὶ τὴν ἐκ μὴ ὑποκειμένου εἰς ὑποκείμενον.	So it follows necessarily from what has been said above that there are only three kinds of change, that from subject to subject, that from subject to non-subject, and that from non-subject to subject:
ἡ γὰρ οὐκ ἐξ ὑποκειμένου εἰς μὴ ὑποκείμενον οὐκ ἔστιν μεταβολὴ διὰ τὸ μὴ εἶναι κατ' ἀντίθεσιν· οὔτε γὰρ ἐναντία οὔτε ἀντίφασίς ἐστιν.	for the fourth conceivable kind, that from non-subject to nonsubject, is not change, as in that case there is no opposition either of contraries or of contradictories.
ἡ μὲν οὖν οὐκ ἐξ ὑποκειμένου εἰς ὑποκείμενον μεταβολὴ κατ' ἀντίφασιν γένεσίς ἐστιν, ἡ μὲν ἁπλῶς ἁπλῆ, ἡ δὲ τὶς τινός (οἷον ἡ μὲν ἐκ μὴ λευκοῦ εἰς λευκὸν γένεσις τούτου, ἡ δ' ἐκ τοῦ μὴ ὄντος ἁπλῶς εἰς οὐσίαν γένεσις ἁπλῶς, καθ' ἣν ἁπλῶς γίγνεσθαι καὶ οὐ τὶ γίγνεσθαι λέγομεν)·	Now change from non-subject to subject, the relation being that of contradiction, is 'coming to be'—'unqualified coming to be' when the change takes place in an unqualified way, 'particular coming to be' when the change is change in a particular character: for instance, a change from not—white to white is a coming to be of the particular thing, white, while change from unqualified not-being to being is coming to be in an unqualified way, in respect of which we say that a thing 'comes to be' without qualification, not that it 'comes to be' some particular thing.
ἡ δ' ἐξ ὑποκειμένου εἰς οὐχ ὑποκεί μενον φθορά, ἁπλῶς μὲν ἡ ἐκ τῆς οὐσίας εἰς τὸ μὴ εἶναι, τὶς δὲ ἡ εἰς τὴν ἀντικειμένην ἀπόφασιν, καθάπερ ἐλέχθη καὶ ἐπὶ τῆς γενέσεως.	Change from subject to non-subject is 'perishing'—'unqualified perishing' when the change is from being to not-being, 'particular perishing' when the change is to the opposite negation, the distinction being the same as that made in the case of coming to be.
εἰ δὴ τὸ μὴ ὂν λέγεται πλεοναχῶς, καὶ μήτε τὸ κατὰ σύνθεσιν ἢ διαίρεσιν ἐνδέχεται κινεῖσθαι μήτε τὸ κατὰ δύναμιν, τὸ τῷ ἁπλῶς κατ' ἐνέργειαν ὄντι ἀντικείμενον (τὸ μὲν γὰρ μὴ λευκὸν ἢ μὴ ἀγαθὸν ὅμως ἐνδέχεται κινεῖσθαι κατὰ συμβεβηκός, εἴη γὰρ <�ἂν> ἄνθρωπος τὸ μὴ λευκόν· τὸ δ' ἁπλῶς μὴ τόδε οὐδαμῶς), ἀδύνατον [γὰρ] τὸ μὴ ὂν κινεῖσθαι (εἰ δὲ τοῦτο, καὶ τὴν γένεσιν κίνησιν εἶναι· γίγνεται γὰρ τὸ μὴ ὄν· εἰ γὰρ καὶ ὅτι μάλιστα κατὰ συμβεβηκὸς γίγνεται, ἀλλ' ὅμως ἀληθὲς εἰπεῖν ὅτι ὑπάρχει τὸ μὴ ὂν κατὰ τοῦ γιγνομένου ἁπλῶς)—ὁμοίως δὲ καὶ τὸ ἠρεμεῖν. ταῦτά τε δὴ συμβαίνει δυσχερῆ [τῷ κινεῖσθαι τὸ μὴ ὄν]	Now the expression 'not-being' is used in several senses: and there can be motion neither of that which 'is not' in respect of the affirmation or negation of a predicate, nor of that which 'is not' in the sense that it only potentially 'is', that is to say the opposite of that which actually 'is' in an unqualified sense: for although that which is 'not-white' or 'not-good' may nevertheless he in motion accidentally (for example that which is 'not-white' might be a man), yet that which is without qualification 'not-so-and-so' cannot in any sense be in motion: therefore it is impossible for that which is not to be in motion. This being so, it follows that 'becoming' cannot be a motion: for it is that which 'is not' that 'becomes'. For however true it may be that it accidentally 'becomes', it is nevertheless correct to say that it is that which 'is not' that in an unqualified sense 'becomes'. And similarly it is impossible for that which 'is not' to be at rest. There are these difficulties, then, in the way of the assumption that that which 'is not' can be in motion:
καὶ εἰ πᾶν τὸ κινούμενον ἐν τόπῳ, τὸ δὲ μὴ ὂν οὐκ ἔστιν ἐν τόπῳ· εἴη γὰρ ἄν που.	and it may be further objected that, whereas everything which is in motion is in space, that which 'is not' is not in space: for then it would be somewhere.
οὐδὲ δὴ ἡ φθορὰ κίνησις· ἐναντίον μὲν γὰρ κινήσει ἢ κίνησις ἢ ἠρεμία, ἡ δὲ φθορὰ γενέσει ἐναντίον.	So, too, 'perishing' is not a motion: for a motion has for its contrary either another motion or rest, whereas 'perishing' is the contrary of 'becoming'.
ἐπεὶ δὲ πᾶσα κίνησις μεταβολή τις, μεταβολαὶ δὲ τρεῖς αἱ εἰρημέναι, τούτων δὲ αἱ κατὰ γένεσιν καὶ φθορὰν (225b.) οὐ κινήσεις, αὗται δ' εἰσὶν αἱ κατ' ἀντίφασιν, ἀνάγκη τὴν ἐξ ὑποκειμένου εἰς ὑποκείμενον μεταβολὴν κίνησιν εἶναι μόνην. τὰ δ' ὑποκείμενα ἢ ἐναντία ἢ μεταξύ (καὶ γὰρ ἡ στέρησις κείσθω ἐναντίον), καὶ δηλοῦται καταφάσει, τὸ γυμνὸν καὶ νωδὸν καὶ μέλαν.	Since, then, every motion is a kind of change, and there are only the three kinds of change mentioned above, and since of these three those which take the form of 'becoming' and 'perishing', that is to say those which imply a relation of contradiction, are not motions: it necessarily follows that only change from subject to subject is motion. And every such subject is either a contrary or an intermediate (for a privation may be allowed to rank as a contrary) and can be affirmatively expressed, as naked, toothless, or black.

Lectio 3
Per se motion is not in other predicaments than quantity, quality, and place

Chapter 1 cont.
εἰ οὖν αἱ κατηγορίαι διῄρηνται οὐσίᾳ καὶ ποιότητι καὶ τῷ ποὺ [καὶ τῷ ποτὲ] καὶ τῷ πρός τι καὶ τῷ ποσῷ καὶ τῷ ποιεῖν ἢ πάσχειν, ἀνάγκη τρεῖς εἶναι κινήσεις, τήν τε τοῦ ποιοῦ καὶ τὴν τοῦ ποσοῦ καὶ τὴν κατὰ τόπον.	If, then, the categories are severally distinguished as Being, Quality, Place, Time, Relation, Quantity, and Activity or Passivity, it necessarily follows that there are three kinds of motion—qualitative, quantitative, and local.
Chapter 2
Κατ' οὐσίαν δ' οὐκ ἔστιν κίνησις διὰ τὸ μηδὲν εἶναι οὐσίᾳ τῶν ὄντων ἐναντίον.	In respect of Substance there is no motion, because Substance has no contrary among things that are.
οὐδὲ δὴ τοῦ πρός τι· ἐνδέχεται γὰρ θατέρου μεταβάλλοντος <�ἀληθεύεσθαι καὶ μὴ> ἀληθεύεσθαι θάτερον μηδὲν μεταβάλλον, ὥστε κατὰ συμβεβηκὸς ἡ κίνησις αὐτῶν.	Nor is there motion in respect of Relation: for it may happen that when one correlative changes, the other, although this does not itself change, is no longer applicable, so that in these cases the motion is accidental.
οὐδὲ δὴ ποιοῦντος καὶ πάσχοντος, ἢ κινουμένου καὶ κινοῦντος, ὅτι οὐκ ἔστι κινήσεως κίνησις οὐδὲ γενέσεως γένεσις, οὐδ' ὅλως μεταβολῆς μεταβολή.	Nor is there motion in respect of Agent and Patient—in fact there can never be motion of mover and moved, because there cannot be motion of motion or becoming of becoming or in general change of change.
πρῶτον μὲν γὰρ διχῶς ἐνδέχεται κινήσεως εἶναι κίνησιν, ἢ ὡς ὑποκειμένου (οἷον ἅνθρωπος κινεῖται ὅτι ἐκ λευκοῦ εἰς μέλαν μεταβάλλει· ἆρά γε οὕτω καὶ ἡ κίνησις ἢ θερμαίνεται ἢ ψύχεται ἢ τόπον ἀλλάττει ἢ αὐξάνεται ἢ φθίνει; τοῦτο δὲ ἀδύνατον· οὐ γὰρ τῶν ὑποκειμένων τι ἡ μεταβολή), ἢ τῷ ἕτερόν τι ὑποκείμενον ἐκ μεταβολῆς μεταβάλλειν εἰς ἕτερον εἶδος [οἷον ἄνθρωπος ἐκ νόσου εἰς ὑγίειαν]. ἀλλ' οὐδὲ τοῦτο δυνατὸν πλὴν κατὰ συμβεβηκός· αὐτὴ γὰρ ἡ κίνησις ἐξ ἄλλου εἴδους εἰς ἄλλο ἐστὶ μεταβολή <�οἷον ἀνθρώπου ἐκ νόσου εἰς ὑγίειαν>· καὶ ἡ γένεσις δὲ καὶ ἡ φθορὰ ὡσαύτως, πλὴν αἱ μὲν εἰς ἀντικείμενα ὡδί, ἡ δὲ ὡδί, ἡ κίνησις. ἅμα οὖν μεταβάλλει ἐξ ὑγιείας εἰς νόσον καὶ ἐξ αὐτῆς ταύτης τῆς μεταβολῆς εἰς ἄλλην. δῆλον δὴ ὅτι ὅταν νοσήσῃ, μεταβεβληκὸς ἔσται εἰς ὁποιανοῦν (ἐνδέχεται γὰρ ἠρεμεῖν), καὶ ἔτι εἰς μὴ τὴν τυχοῦσαν αἰεί, κἀκείνη ἔκ τινος εἴς τι ἕτερον ἔσται, ὥστε καὶ ἡ ἀντι κειμένη ἔσται ὑγίανσις· ἀλλὰ τῷ συμβεβηκέναι, οἷον ἐξ ἀναμνήσεως εἰς λήθην μεταβάλλει, ὅτι ᾧ ὑπάρχει, ἐκεῖνο μεταβάλλει ὁτὲ μὲν εἰς ἐπιστήμην ὁτὲ δ' εἰς ἄγνοιαν.	For in the first place there are two senses in which motion of motion is conceivable. (1) The motion of which there is motion might be conceived as subject; e.g. a man is in motion because he changes from fair to dark. Can it be that in this sense motion grows hot or cold, or changes place, or increases or decreases? Impossible: for change is not a subject. Or (2) can there be motion of motion in the sense that some other subject changes from a change to another mode of being, as e.g. a man changes from falling ill to getting well? Even this is possible only in an accidental sense. For, whatever the subject may be, movement is change from one form to another. (And the same holds good of becoming and perishing, except that in these processes we have a change to a particular kind of opposite, while the other, motion, is a change to a different kind.) So, if there is to be motion of motion, that which is changing from health to sickness must simultaneously be changing from this very change to another. It is clear, then, that by the time that it has become sick, it must also have changed to whatever may be the other change concerned (for that it should be at rest, though logically possible, is excluded by the theory). Moreover this other can never be any casual change, but must be a change from something definite to some other definite thing. So in this case it must be the opposite change, viz. convalescence. It is only accidentally that there can be change of change, e.g. there is a change from remembering to forgetting only because the subject of this change changes at one time to knowledge, at another to ignorance.
ἔτι εἰς ἄπειρον βαδιεῖται, εἰ ἔσται μεταβολῆς μεταβολὴ καὶ γενέσεως γένεσις. ἀνάγκη δὴ καὶ τὴν προτέραν, εἰ ἡ ὑστέρα (226a.) ἔσται, οἷον εἰ ἡ ἁπλῆ γένεσις ἐγίγνετό ποτε, καὶ τὸ γιγνόμενον ἐγίγνετο, ὥστε οὔπω ἦν τὸ γιγνόμενον ἁπλῶς, ἀλλά τι γιγνόμενον γιγνόμενον ἤδη, καὶ πάλιν τοῦτ' ἐγίγνετό ποτε, ὥστ' οὐκ ἦν πω τότε γιγνόμενον γιγνόμενον. ἐπεὶ δὲ τῶν ἀπείρων οὐκ ἔστιν τι πρῶτον, οὐκ ἔσται τὸ πρῶτον, ὥστ' οὐδὲ τὸ ἐχόμενον· οὔτε γί γνεσθαι οὖν οὔτε κινεῖσθαι οἷόν τε οὔτε μεταβάλλειν οὐδέν.	In the second place, if there is to be change of change and becoming of becoming, we shall have an infinite regress. Thus if one of a series of changes is to be a change of change, the preceding change must also be so: e.g. if simple becoming was ever in process of becoming, then that which was becoming simple becoming was also in process of becoming, so that we should not yet have arrived at what was in process of simple becoming but only at what was already in process of becoming in process of becoming. And this again was sometime in process of becoming, so that even then we should not have arrived at what was in process of simple becoming. And since in an infinite series there is no first term, here there will be no first stage and therefore no following stage either. On this hypothesis, then, nothing can become or be moved or change.
ἔτι τοῦ αὐτοῦ κίνησις ἡ ἐναντία (καὶ ἔτι ἠρέμησις), καὶ γένεσις καὶ φθορά, ὥστε τὸ γιγνόμενον γιγνόμενον ὅταν γένηται γιγνόμενον, τότε φθείρεται· οὔτε γὰρ εὐθὺς γιγνόμενον οὔθ' ὕστερον· εἶναι γὰρ δεῖ τὸ φθειρόμενον.	Thirdly, if a thing is capable of any particular motion, it is also capable of the corresponding contrary motion or the corresponding coming to rest, and a thing that is capable of becoming is also capable of perishing: consequently, if there be becoming of becoming, that which is in process of becoming is in process of perishing at the very moment when it has reached the stage of becoming: since it cannot be in process of perishing when it is just beginning to become or after it has ceased to become: for that which is in process of perishing must be in existence.
ἔτι ὕλην δεῖ ὑπεῖναι καὶ τῷ γιγνομένῳ καὶ τῷ μεταβάλλοντι. τίς οὖν ἔσται—ὥσπερ τὸ ἀλλοιωτὸν σῶμα ἢ ψυχή, οὕτω τί τὸ γιγνόμενον κίνησις ἢ γένεσις; καὶ πάλιν τί εἰς ὃ κινοῦνται; δεῖ γὰρ εἶναι [τι] τὴν τοῦδε ἐκ τοῦδε εἰς τόδε κίνησιν [καὶ μὴ κίνησιν] ἢ γένεσιν.	Fourthly, there must be a substrate underlying all processes of becoming and changing. What can this be in the present case? It is either the body or the soul that undergoes alteration: what is it that correspondingly becomes motion or becoming? And again what is the goal of their motion? It must be the motion or becoming of something from something to something else.
ἅμα δὲ πῶς καὶ ἔσται; οὐ γὰρ ἔσται μάθησις ἡ τῆς μαθήσεως γένεσις, ὥστ' οὐδὲ γενέσεως γένεσις, οὐδέ τις τινός.	But in what sense can this be so? For the becoming of learning cannot be learning: so neither can the becoming of becoming be becoming, nor can the becoming of any process be that process.
ἔτι εἰ τρία εἴδη κινήσεώς ἐστιν, τούτων τινὰ ἀνάγκη εἶναι καὶ τὴν ὑποκειμένην φύσιν καὶ εἰς ἃ κινοῦνται, οἷον τὴν φορὰν ἀλλοιοῦσθαι ἢ φέρεσθαι.	Finally, since there are three kinds of motion, the substratum and the goal of motion must be one or other of these, e.g. locomotion will have to be altered or to be locally moved.
ὅλως δὲ ἐπεὶ κινεῖται [τὸ κινούμενον] πᾶν τριχῶς, ἢ κατὰ συμβεβηκὸς ἢ τῷ μέρος τι ἢ [τῷ] καθ' αὑτό, κατὰ συμβεβηκὸς μόνον ἂν ἐνδέχοιτο μεταβάλλειν τὴν μεταβολήν, οἷον εἰ ὁ ὑγιαζόμενος τρέχοι ἢ μανθάνοι· τὴν δὲ κατὰ συμβεβηκὸς ἀφεῖμεν πάλαι.	To sum up, then, since everything that is moved is moved in one of three ways, either accidentally, or partially, or essentially, change can change only accidentally, as e.g. when a man who is being restored to health runs or learns: and accidental change we have long ago decided to leave out of account.

Lectio 4
Motion is solely in quantity, quality, and place

Chapter 2 cont.
ἐπεὶ δὲ οὔτε οὐσίας οὔτε τοῦ πρός τι οὔτε τοῦ ποιεῖν καὶ πάσχειν, λείπεται κατὰ τὸ ποιὸν καὶ τὸ ποσὸν καὶ τὸ ποὺ κίνησιν εἶναι μόνον· ἐν ἑκάστῳ γὰρ ἔστι τούτων ἐναντίωσις.	Since, then, motion can belong neither to Being nor to Relation nor to Agent and Patient, it remains that there can be motion only in respect of Quality, Quantity, and Place: for with each of these we have a pair of contraries.
ἡ μὲν οὖν κατὰ τὸ ποιὸν κίνησις ἀλλοίωσις ἔστω· τοῦτο γὰρ ἐπέζευκται κοινὸν ὄνομα. λέγω δὲ τὸ ποιὸν οὐ τὸ ἐν τῇ οὐσίᾳ (καὶ γὰρ ἡ διαφορὰ ποιότης) ἀλλὰ τὸ παθητικόν, καθ' ὃ λέγεται πάσχειν ἢ ἀπαθὲς εἶναι.	Motion in respect of Quality let us call alteration, a general designation that is used to include both contraries: and by Quality I do not here mean a property of substance (in that sense that which constitutes a specific distinction is a quality) but a passive quality in virtue of which a thing is said to be acted on or to be incapable of being acted on.
ἡ δὲ κατὰ τὸ ποσὸν τὸ μὲν κοινὸν ἀνώνυμος, καθ' ἑκάτερον δ' αὔξησις καὶ φθίσις, ἡ μὲν εἰς τὸ τέλειον μέγεθος αὔξησις, ἡ δ' ἐκ τούτου φθίσις.	Motion in respect of Quantity has no name that includes both contraries, but it is called increase or decrease according as one or the other is designated: that is to say motion in the direction of complete magnitude is increase, motion in the contrary direction is decrease.
ἡ δὲ κατὰ τόπον καὶ τὸ κοινὸν καὶ τὸ ἴδιον ἀνώνυμος, ἔστω δὲ φορὰ καλουμένη τὸ κοινόν· καίτοι λέγεταί γε ταῦτα φέρεσθαι μόνα κυρίως, ὅταν μὴ ἐφ' αὑτοῖς ᾖ τὸ στῆναι τοῖς μεταβάλλουσι τὸν τόπον, καὶ ὅσα (226b.) μὴ αὐτὰ ἑαυτὰ κινεῖ κατὰ τόπον.	Motion in respect of Place has no name either general or particular: but we may designate it by the general name of locomotion, though strictly the term 'locomotion' is applicable to things that change their place only when they have not the power to come to a stand, and to things that do not move themselves locally.
ἡ δ' ἐν τῷ αὐτῷ εἴδει μεταβολὴ ἐπὶ τὸ μᾶλλον καὶ ἧττον ἀλλοίωσίς ἐστιν· ἢ γὰρ ἐξ ἐναντίου ἢ εἰς ἐναντίον κίνησίς ἐστιν, ἢ ἁπλῶς ἢ πῄ· ἐπὶ μὲν γὰρ τὸ ἧττον ἰοῦσα εἰς τοὐναντίον λεχθήσεται μεταβάλλειν, ἐπὶ δὲ τὸ μᾶλλον ὡς ἐκ τοὐναντίου εἰς αὐτό. διαφέρει γὰρ οὐδὲν πῂ μεταβάλλειν ἢ ἁπλῶς, πλὴν πῂ δεήσει τἀναντία ὑπάρχειν· τὸ δὲ μᾶλλον καὶ ἧττόν ἐστι τὸ πλέον ἢ ἔλαττον ἐνυπάρχειν τοῦ ἐναντίου καὶ μή.	Change within the same kind from a lesser to a greater or from a greater to a lesser degree is alteration: for it is motion either from a contrary or to a contrary, whether in an unqualified or in a qualified sense: for change to a lesser degree of a quality will be called change to the contrary of that quality, and change to a greater degree of a quality will be regarded as change from the contrary of that quality to the quality itself. It makes no difference whether the change be qualified or unqualified, except that in the former case the contraries will have to be contrary to one another only in a qualified sense: and a thing's possessing a quality in a greater or in a lesser degree means the presence or absence in it of more or less of the opposite quality.
ὅτι μὲν οὖν αὗται τρεῖς μόναι κινήσεις εἰσίν, ἐκ τούτων δῆλον·	It is now clear, then, that there are only these three kinds of motion.
ἀκίνητον δ' ἐστὶ τό τε ὅλως ἀδύνατον κινηθῆναι, ὥσπερ ὁ ψόφος ἀόρατος, καὶ τὸ ἐν πολλῷ χρόνῳ μόλις κινούμενον ἢ τὸ βραδέως ἀρχόμενον, ὃ λέγεται δυσκίνητον, καὶ τὸ πεφυκὸς μὲν κινεῖσθαι καὶ δυνάμενον, μὴ κινούμενον δὲ τότε ὅτε πέφυκε καὶ οὗ καὶ ὥς, ὅπερ ἠρεμεῖν καλῶ τῶν ἀκινήτων μόνον· ἐναντίον γὰρ ἠρεμία κινήσει, ὥστε στέρησις ἂν εἴη τοῦ δεκτικοῦ.	The term 'immovable' we apply in the first place to that which is absolutely incapable of being moved (just as we correspondingly apply the term invisible to sound); in the second place to that which is moved with difficulty after a long time or whose movement is slow at the start—in fact, what we describe as hard to move; and in the third place to that which is naturally designed for and capable of motion, but is not in motion when, where, and as it naturally would be so. This last is the only kind of immovable thing of which I use the term 'being at rest': for rest is contrary to motion, so that rest will be negation of motion in that which is capable of admitting motion.
τί μὲν οὖν ἐστι κίνησις καὶ τί ἠρεμία, καὶ πόσαι μεταβολαὶ καὶ ποῖαι κινήσεις, φανερὸν ἐκ τῶν εἰρημένων.	The foregoing remarks are sufficient to explain the essential nature of motion and rest, the number of kinds of change, and the different varieties of motion.

Lectio 5
The definitions of “in contact,” “consecutive,” “continuous”

Chapter 3
Μετὰ δὲ ταῦτα λέγωμεν τί ἐστιν τὸ ἅμα καὶ χωρίς, καὶ τί τὸ ἅπτεσθαι, καὶ τί τὸ μεταξὺ καὶ τί τὸ ἐφεξῆς καὶ τί τὸ ἐχόμενον καὶ συνεχές, καὶ τοῖς ποίοις ἕκαστον τούτων ὑπάρχειν πέφυκεν.	Let us now proceed to define the terms 'together' and 'apart', 'in contact', 'between', 'in succession', 'contiguous', and 'continuous', and to show in what circumstances each of these terms is naturally applicable.
ἅμα μὲν οὖν λέγω ταῦτ' εἶναι κατὰ τόπον, ὅσα ἐν ἑνὶ τόπῳ ἐστὶ πρώτῳ, χωρὶς δὲ ὅσα ἐν ἑτέρῳ, ἅπτεσθαι δὲ ὧν τὰ ἄκρα ἅμα.	Things are said to be together in place when they are in one place (in the strictest sense of the word 'place') and to be apart when they are in different places. Things are said to be in contact when their extremities are together.
μεταξὺ δὲ εἰς ὃ πέφυκε πρότερον ἀφικνεῖσθαι τὸ μεταβάλλον ἢ εἰς ὃ ἔσχατον μεταβάλλει κατὰ φύσιν συνεχῶς μεταβάλλον. [ἐν ἐλαχίστοις δ' ἐστι τὸ μεταξὺ τρισίν· ἔσχατον μὲν γάρ ἐστι τῆς μεταβολῆς τὸ εναντιον.] συνεχῶς δὲ κινεῖται τὸ μηθὲν ἢ ὅτι ὀλίγιστον διαλεῖπον τοῦ πράγματος—μὴ τοῦ χρόνου (οὐδὲν γὰρ κωλύει διαλείποντα, καὶ εὐθὺς δὲ μετὰ τὴν ὑπάτην φθέγξασθαι τὴν νεάτην) ἀλλὰ τοῦ πράγματος ἐν ᾧ κινεῖται. [<�ἐπεὶ δὲ πᾶσα μεταβολὴ ἐν τοῖς ἀντικειμένοις, τὰ δ' ἀντικείμενα τά τε ἐναντία καὶ τὰ κατὰ ἀντίφασιν, ἀντιφάσεως δ' οὐδὲν ἀνὰ μέσον, φανερὸν ὅτι ἐν τοῖς ἐναντίοις ἔσται τὸ μεταξύ. (226b.) ἐν ἐλαχίστοις δ' ἐστὶ τὸ μεταξὺ τρισίν· ἔσχατον μὲν γάρ ἐστι τῆς μεταβολῆς τὸ ἐναντίον,>] τοῦτο δὲ ἔν τε ταῖς κατὰ τόπον καὶ ἐν ταῖς ἄλλαις μεταβολαῖς φανερόν. ἐναντίον δὲ κατὰ τόπον τὸ κατ' εὐθεῖαν ἀπέχον πλεῖστον· ἡ γὰρ ἐλαχίστη πεπέρανται, μέτρον δὲ τὸ πεπερασμένον.	That which a changing thing, if it changes continuously in a natural manner, naturally reaches before it reaches that to which it changes last, is between. Thus 'between' implies the presence of at least three things: for in a process of change it is the contrary that is 'last': and a thing is moved continuously if it leaves no gap or only the smallest possible gap in the material—not in the time (for a gap in the time does not prevent things having a 'between', while, on the other hand, there is nothing to prevent the highest note sounding immediately after the lowest) but in the material in which the motion takes place. This is manifestly true not only in local changes but in every other kind as well. (Now every change implies a pair of opposites, and opposites may be either contraries or contradictories; since then contradiction admits of no mean term, it is obvious that 'between' must imply a pair of contraries) That is locally contrary which is most distant in a straight line: for the shortest line is definitely limited, and that which is definitely limited constitutes a measure.
ἐφεξῆς δὲ οὗ μετὰ τὴν ἀρχὴν ὄντος ἢ θέσει ἢ εἴδει ἢ ἄλλῳ τινὶ οὕτως ἀφορισθέντος (227a.) μηδὲν μεταξύ ἐστι τῶν ἐν ταὐτῷ γένει καὶ οὗ ἐφεξῆς ἐστιν (λέγω δ' οἷον γραμμὴ γραμμῆς ἢ γραμμαί, ἢ μονάδος μονὰς ἢ μονάδες, ἢ οἰκίας οἰκία· ἄλλο δ' οὐδὲν κωλύει μεταξὺ εἶναι). τὸ γὰρ ἐφεξῆς τινὶ ἐφεξῆς καὶ ὕστερόν τι· οὐ γὰρ τὸ ἓν ἐφεξῆς τοῖν δυοῖν, οὐδ' ἡ νουμηνία τῇ δευτέρᾳ ἐφεξῆς, ἀλλὰ ταῦτ' ἐκείνοις. ἐχόμενον δὲ ὃ ἂν ἐφεξῆς ὂν ἅπτηται.	A thing is 'in succession' when it is after the beginning in position or in form or in some other respect in which it is definitely so regarded, and when further there is nothing of the same kind as itself between it and that to which it is in succession, e.g. a line or lines if it is a line, a unit or units if it is a unit, a house if it is a house (there is nothing to prevent something of a different kind being between). For that which is in succession is in succession to a particular thing, and is something posterior: for one is not 'in succession' to two, nor is the first day of the month to be second: in each case the latter is 'in succession' to the former. A thing that is in succession and touches is 'contiguous'.
Quoniam autem omnis mutatio in oppositis est, opposita autem sunt et contraria et quae secundum contradictionem sunt, contradictionis autem nihil est medium; menifestum est quod in contrariis erit medium.	Since all change is between opposites, while opposites include both the contrary and the contradictory, and there is no mean between contradictories, it is clear that there is a mean between contraries.
τὸ δὲ συνεχὲς ἔστι μὲν ὅπερ ἐχόμενόν τι, λέγω δ' εἶναι συνεχὲς ὅταν ταὐτὸ γένηται καὶ ἓν τὸ ἑκατέρου πέρας οἷς ἅπτονται, καὶ ὥσπερ σημαίνει τοὔνομα, συνέχηται. τοῦτο δ' οὐχ οἷόν τε δυοῖν ὄντοιν εἶναι τοῖν ἐσχάτοιν. τούτου δὲ διωρισμένου φανερὸν ὅτι ἐν τούτοις ἐστὶ τὸ συνεχές, ἐξ ὧν ἕν τι πέφυκε γίγνεσθαι κατὰ τὴν σύναψιν. καὶ ὥς ποτε γίγνεται τὸ συνέχον ἕν, οὕτω καὶ τὸ ὅλον ἔσται ἕν, οἷον ἢ γόμφῳ ἢ κόλλῃ ἢ ἁφῇ ἢ προσφύσει.	The 'continuous' is a subdivision of the contiguous: things are called continuous when the touching limits of each become one and the same and are, as the word implies, contained in each other: continuity is impossible if these extremities are two. This definition makes it plain that continuity belongs to things that naturally in virtue of their mutual contact form a unity. And in whatever way that which holds them together is one, so too will the whole be one, e.g. by a rivet or glue or contact or organic union.
φανερὸν δὲ καὶ ὅτι πρῶτον τὸ ἐφεξῆς ἐστι· τὸ μὲν γὰρ ἁπτόμενον ἐφεξῆς ἀνάγκη εἶναι, τὸ δ' ἐφεξῆς οὐ πᾶν ἅπτεσθαι (διὸ καὶ ἐν προτέροις τῷ λόγῳ τὸ ἐφεξῆς ἔστιν, οἷον ἐν ἀριθμοῖς, ἁφὴ δ' οὐκ ἔστιν),	It is obvious that of these terms 'in succession' is first in order of analysis: for that which touches is necessarily in succession, but not everything that is in succession touches: and so succession is a property of things prior in definition, e.g. numbers, while contact is not.
καὶ εἰ μὲν συνεχές, ἀνάγκη ἅπτεσθαι, εἰ δ' ἅπτεται, οὔπω συνεχές· οὐ γὰρ ἀνάγκη ἓν εἶναι αὐτῶν τὰ ἄκρα, εἰ ἅμα εἶεν· ἀλλ' εἰ ἕν, ἀνάγκη καὶ ἅμα. ὥστε ἡ σύμφυσις ὑστάτη κατὰ τὴν γένεσιν· ἀνάγκη γὰρ ἅψασθαι εἰ συμφύσεται τὰ ἄκρα, τὰ δὲ ἁπτόμενα οὐ πάντα συμπέφυκεν· ἐν οἷς δὲ μὴ ἔστιν ἁφή, δῆλον ὅτι οὐκ ἔστιν οὐδὲ σύμφυσις ἐν τούτοις.	And if there is continuity there is necessarily contact, but if there is contact, that alone does not imply continuity: for the extremities of things may be 'together' without necessarily being one: but they cannot be one without being necessarily together. So natural junction is last in coming to be: for the extremities must necessarily come into contact if they are to be naturally joined: but things that are in contact are not all naturally joined, while there is no contact clearly there is no natural junction either.
ὥστ' εἰ ἔστι στιγμὴ καὶ μονὰς οἵας λέγουσι κεχωρισμένας, οὐχ οἷόν τε εἶναι μονάδα καὶ στιγμὴν τὸ αὐτό· ταῖς μὲν γὰρ ὑπάρχει τὸ ἅπτεσθαι, ταῖς δὲ μονάσιν τὸ ἐφεξῆς, καὶ τῶν μὲν ἐνδέχεται εἶναί τι μεταξύ (πᾶσα γὰρ γραμμὴ μεταξὺ στιγμῶν), τῶν δ' οὐκ ἀνάγκη· οὐδὲ γὰρ μεταξὺ δυάδος καὶ μονάδος.	Hence, if as some say 'point' and 'unit' have an independent existence of their own, it is impossible for the two to be identical: for points can touch while units can only be in succession. Moreover, there can always be something between points (for all lines are intermediate between points), whereas it is not necessary that there should possibly be anything between units: for there can be nothing between the numbers one and two.
τί μὲν οὖν ἐστι τὸ ἅμα καὶ χωρίς, καὶ τί τὸ ἅπτεσθαι, καὶ τί τὸ μεταξὺ (227b.) καὶ τὸ ἐφεξῆς, καὶ τί τὸ ἐχόμενον καὶ τὸ συνεχές, καὶ τοῖς ποίοις ἕκαστον τούτων ὑπάρχει, εἴρηται. Μία δὲ κίνησις λέγεται πολλαχῶς· τὸ γὰρ ἓν πολλαχῶς λέγομεν.	We have now defined what is meant by 'together' and 'apart', 'contact', 'between' and 'in succession', 'contiguous' and 'continuous': and we have shown in what circumstances each of these terms is applicable.

Lectio 6
Generic, specific, and numerical unity of motion

Chapter 4
γένει μὲν οὖν μία κατὰ τὰ σχήματα τῆς κατηγορίας ἐστί (φορὰ μὲν γὰρ πάσῃ φορᾷ τῷ γένει μία, ἀλλοίωσις δὲ φορᾶς ἑτέρα τῷ γένει),	There are many senses in which motion is said to be 'one': for we use the term 'one' in many senses. Motion is one generically according to the different categories to which it may be assigned: thus any locomotion is one generically with any other locomotion, whereas alteration is different generically from locomotion.
εἴδει δὲ μία, ὅταν τῷ γένει μία οὖσα καὶ ἐν ἀτόμῳ εἴδει ᾖ. οἷον χρώματος μὲν εἰσὶ διαφοραί—τοιγαροῦν ἄλλη τῷ εἴδει μέλανσις καὶ λεύκανσις [πᾶσα οὖν λεύκανσις πάσῃ λευκάνσει ἡ αὐτὴ κατ' εἶδος ἔσται καὶ πᾶσα μέλανσις μελάνσει]—λευκότητος δ' οὐκέτι· διὸ τῷ εἴδει μία λεύκανσις λευκάνσει πάσῃ. εἰ δ' ἔστιν ἄτθ' ἃ καὶ γένη ἅμα καὶ εἴδη ἐστίν, δῆλον ὡς ἔστιν ὡς εἴδει μία ἔσται, ἁπλῶς δὲ μία εἴδει οὔ, οἷον ἡ μάθησις, εἰ ἡ ἐπιστήμη εἶδος μὲν ὑπολήψεως, γένος δὲ τῶν ἐπιστημῶν.	Motion is one specifically when besides being one generically it also takes place in a species incapable of subdivision: e.g. colour has specific differences: therefore blackening and whitening differ specifically; but at all events every whitening will be specifically the same with every other whitening and every blackening with every other blackening. But white is not further subdivided by specific differences: hence any whitening is specifically one with any other whitening. Where it happens that the genus is at the same time a species, it is clear that the motion will then in a sense be one specifically though not in an unqualified sense: learning is an example of this, knowledge being on the one hand a species of apprehension and on the other hand a genus including the various knowledges.
ἀπορήσειε δ' ἄν τις εἰ εἴδει μία <�ἡ> κίνησις, ὅταν ἐκ τοῦ αὐτοῦ τὸ αὐτὸ εἰς τὸ αὐτὸ μεταβάλλῃ, οἷον ἡ μία στιγμὴ ἐκ τοῦδε τοῦ τόπου εἰς τόνδε τὸν τόπον πάλιν καὶ πάλιν. εἰ δὲ τοῦτ', ἔσται ἡ κυκλοφορία τῇ εὐθυφορίᾳ ἡ αὐτὴ καὶ ἡ κύλισις τῇ βαδίσει. ἢ διώρισται, τὸ ἐν ᾧ ἂν ἕτερον ᾖ τῷ εἴδει, ὅτι ἑτέρα ἡ κίνησις, τὸ δὲ περιφερὲς τοῦ εὐθέος ἕτερον τῷ εἴδει; γένει μὲν οὖν καὶ εἴδει κίνησις μία οὕτως,	A difficulty, however, may be raised as to whether a motion is specifically one when the same thing changes from the same to the same, e.g. when one point changes again and again from a particular place to a particular place: if this motion is specifically one, circular motion will be the same as rectilinear motion, and rolling the same as walking. But is not this difficulty removed by the principle already laid down that if that in which the motion takes place is specifically different (as in the present instance the circular path is specifically different from the straight) the motion itself is also different? We have explained, then, what is meant by saying that motion is one generically or one specifically.
ἁπλῶς δὲ μία κίνησις ἡ τῇ οὐσίᾳ μία καὶ τῷ ἀριθμῷ· τίς δ' ἡ τοιαύτη, δῆλον διελομένοις. τρία γάρ ἐστι τὸν ἀριθμὸν περὶ ἃ λέγομεν τὴν κίνησιν, ὃ καὶ ἐν ᾧ καὶ ὅτε. λέγω δ' ὅτι ἀνάγκη εἶναί τι τὸ κινούμενον, οἷον ἄνθρωπον ἢ χρυσόν, καὶ ἔν τινι τοῦτο κινεῖσθαι, οἷον ἐν τόπῳ ἢ ἐν πάθει, καὶ ποτέ· ἐν χρόνῳ γὰρ πᾶν κινεῖται. τούτων δὲ τὸ μὲν εἶναι τῷ γένει ἢ τῷ εἴδει μίαν ἐστὶν ἐν τῷ πράγματι ἐν ᾧ κινεῖται, τὸ δ' ἐχομένην ἐν τῷ χρόνῳ, τὸ δ' ἁπλῶς μίαν ἐν ἅπασι τούτοις· καὶ ἐν ᾧ γὰρ ἓν δεῖ εἶναι καὶ ἄτομον, οἷον τὸ εἶδος, καὶ τὸ ὅτε, οἷον τὸν χρόνον ἕνα καὶ μὴ διαλείπειν, καὶ τὸ κινούμενον ἓν εἶναι μὴ κατὰ συμβεβηκός, ὥσπερ τὸ λευκὸν μελαίνεσθαι καὶ Κορίσκον βαδίζειν (ἓν δὲ Κορίσκος καὶ λευκόν, ἀλλὰ κατὰ συμβεβηκός), (228a.) μηδὲ κοινόν· εἴη γὰρ ἂν ἅμα δύο ἀνθρώπους ὑγιάζεσθαι τὴν αὐτὴν ὑγίανσιν, οἷον ὀφθαλμίας· ἀλλ' οὐ μία αὕτη, ἀλλ' εἴδει μία.	Motion is one in an unqualified sense when it is one essentially or numerically: and the following distinctions will make clear what this kind of motion is. There are three classes of things in connexion with which we speak of motion, the 'that which', the 'that in which', and the 'that during which'. I mean that there must he something that is in motion, e.g. a man or gold, and it must be in motion in something, e.g. a place or an affection, and during something, for all motion takes place during a time. Of these three it is the thing in which the motion takes place that makes it one generically or specifically, it is the thing moved that makes the motion one in subject, and it is the time that makes it consecutive: but it is the three together that make it one without qualification: to effect this, that in which the motion takes place (the species) must be one and incapable of subdivision, that during which it takes place (the time) must be one and unintermittent, and that which is in motion must be one—not in an accidental sense (i.e. it must be one as the white that blackens is one or Coriscus who walks is one, not in the accidental sense in which Coriscus and white may be one), nor merely in virtue of community of nature (for there might be a case of two men being restored to health at the same time in the same way, e.g. from inflammation of the eye, yet this motion is not really one, but only specifically one).
τὸ δὲ Σωκράτη τὴν αὐτὴν μὲν ἀλλοίωσιν ἀλλοιοῦσθαι τῷ εἴδει, ἐν ἄλλῳ δὲ χρόνῳ καὶ πάλιν ἐν ἄλλῳ, εἰ μὲν ἐνδέχεται τὸ φθαρὲν πάλιν ἓν γίγνεσθαι τῷ ἀριθμῷ, εἴη ἂν καὶ αὕτη μία, εἰ δὲ μή, ἡ αὐτὴ μέν, μία δ' οὔ.	Suppose, however, that Socrates undergoes an alteration specifically the same but at one time and again at another: in this case if it is possible for that which ceased to be again to come into being and remain numerically the same, then this motion too will be one: otherwise it will be the same but not one.
ἔχει δ' ἀπορίαν ταύτῃ παραπλησίαν καὶ πότερον μία ἡ ὑγίεια καὶ ὅλως αἱ ἕξεις καὶ τὰ πάθη τῇ οὐσίᾳ εἰσὶν ἐν τοῖς σώμασιν· κινούμενα γὰρ φαίνεται τὰ ἔχοντα καὶ ῥέοντα. εἰ δὴ ἡ αὐτὴ καὶ μία ἡ ἕωθεν καὶ νῦν ὑγίεια, διὰ τί οὐκ ἂν καὶ ὅταν διαλιπὼν λάβῃ πάλιν τὴν ὑγίειαν, καὶ αὕτη κἀκείνη μία τῷ ἀριθμῷ ἂν εἴη;	And akin to this difficulty there is another; viz. is health one? and generally are the states and affections in bodies severally one in essence although (as is clear) the things that contain them are obviously in motion and in flux? Thus if a person's health at daybreak and at the present moment is one and the same, why should not this health be numerically one with that which he recovers after an interval?
ὁ γὰρ αὐτὸς λόγος· πλὴν τοσοῦτον διαφέρει, ὅτι εἰ μὲν δύο, δι' αὐτὸ τοῦτο, ὡς τῷ ἀριθμῷ, καὶ τὰς ἐνεργείας ἀνάγκη (μία γὰρ ἀριθμῷ ἐνέργεια ἑνὸς ἀριθμῷ)· εἰ δ' ἡ ἕξις μία, ἴσως οὐκ ἄν τῳ δόξειέ πω μία καὶ ἡ ἐνέργεια εἶναι (ὅταν γὰρ παύσηται βαδίζων, οὐκέτι ἔστιν ἡ βάδισις, πάλιν δὲ βαδίζοντος ἔσται). εἰ δ' οὖν μία καὶ ἡ αὐτή, ἐνδέχοιτ' ἂν τὸ αὐτὸ καὶ ἓν καὶ φθείρεσθαι καὶ εἶναι πολλάκις. αὗται μὲν οὖν εἰσιν αἱ ἀπορίαι ἔξω τῆς νῦν σκέψεως·	The same argument applies in each case. There is, however, we may answer, this difference: that if the states are two then it follows simply from this fact that the activities must also in point of number be two (for only that which is numerically one can give rise to an activity that is numerically one), but if the state is one, this is not in itself enough to make us regard the activity also as one: for when a man ceases walking, the walking no longer is, but it will again be if he begins to walk again. But, be this as it may, if in the above instance the health is one and the same, then it must be possible for that which is one and the same to come to be and to cease to be many times. However, these difficulties lie outside our present inquiry.

Lectio 7
Numerical unity of motion (continued)

Chapter 4 cont.
ἐπεὶ δὲ συνεχὴς πᾶσα κίνησις, τήν τε ἁπλῶς μίαν ἀνάγκη καὶ συνεχῆ εἶναι, εἴπερ πᾶσα διαιρετή, καὶ εἰ συνεχής, μίαν. οὐ γὰρ πᾶσα γένοιτ' ἂν συνεχὴς πάσῃ, ὥσπερ οὐδ' ἄλλο οὐδὲν τῷ τυχόντι τὸ τυχόν, ἀλλ' ὅσων ἓν τὰ ἔσχατα. ἔσχατα δὲ τῶν μὲν οὐκ ἔστι, τῶν δ' ἔστιν ἄλλα τῷ εἴδει καὶ ὁμώνυμα· πῶς γὰρ ἂν ἅψαιτο ἢ ἓν γένοιτο τὸ ἔσχατον γραμμῆς καὶ βαδίσεως; ἐχόμεναι μὲν οὖν εἶεν ἂν καὶ αἱ μὴ αἱ αὐταὶ τῷ εἴδει μηδὲ τῷ γένει (δραμὼν γὰρ ἄν τις πυρέξειεν εὐθύς), καὶ οἷον ἡ λαμπὰς <�ἡ> ἐκ διαδοχῆς φορὰ ἐχομένη, συνεχὴς δ' οὔ. κεῖται γὰρ τὸ συνεχές, ὧν τὰ ἔσχατα ἕν. ὥστ' ἐχόμεναι καὶ ἐφεξῆς εἰσὶ τῷ τὸν χρό νον εἶναι συνεχῆ, συνεχὴς δὲ τῷ τὰς κινήσεις· τοῦτο δ', (228b.) ὅταν ἓν τὸ ἔσχατον γένηται ἀμφοῖν. διὸ ἀνάγκη τὴν αὐτὴν εἶναι τῷ εἴδει καὶ ἑνὸς καὶ ἐν ἑνὶ χρόνῳ τὴν ἁπλῶς συνεχῆ κίνησιν καὶ μίαν, τῷ χρόνῳ μέν, ὅπως μὴ ἀκινησία μεταξὺ ᾖ (ἐν τῷ διαλείποντι γὰρ ἠρεμεῖν ἀνάγκη· πολλαὶ οὖν καὶ οὐ μία ἡ κίνησις, ὧν ἐστὶν ἠρεμία μεταξύ, ὥστε εἴ τις κίνησις στάσει διαλαμβάνεται, οὐ μία οὐδὲ συνεχής· διαλαμβάνεται δέ, εἰ μεταξὺ χρόνος)· τῆς δὲ τῷ εἴδει μὴ μιᾶς, καὶ εἰ μὴ διαλείπεται [ὁ χρόνος], ὁ μὲν [γὰρ] χρόνος εἷς, τῷ εἴδει δ' ἡ κίνησις ἄλλη· τὴν μὲν γὰρ μίαν ἀνάγκη καὶ τῷ εἴδει μίαν εἶναι, ταύτην δ' ἁπλῶς μίαν οὐκ ἀνάγκη. τίς μὲν οὖν κίνησις ἁπλῶς μία, εἴρηται·	Since every motion is continuous, a motion that is one in an unqualified sense must (since every motion is divisible) be continuous, and a continuous motion must be one. There will not be continuity between any motion and any other indiscriminately any more than there is between any two things chosen at random in any other sphere: there can be continuity only when the extremities of the two things are one. Now some things have no extremities at all: and the extremities of others differ specifically although we give them the same name of 'end': how should e.g. the 'end' of a line and the 'end' of walking touch or come to be one? Motions that are not the same either specifically or generically may, it is true, be consecutive (e.g. a man may run and then at once fall ill of a fever), and again, in the torch-race we have consecutive but not continuous locomotion: for according to our definition there can be continuity only when the ends of the two things are one. Hence motions may be consecutive or successive in virtue of the time being continuous, but there can be continuity only in virtue of the motions themselves being continuous, that is when the end of each is one with the end of the other. Motion, therefore, that is in an unqualified sense continuous and one must be specifically the same, of one thing, and in one time. Unity is required in respect of time in order that there may be no interval of immobility, for where there is intermission of motion there must be rest, and a motion that includes intervals of rest will be not one but many, so that a motion that is interrupted by stationariness is not one or continuous, and it is so interrupted if there is an interval of time. And though of a motion that is not specifically one (even if the time is unintermittent) the time is one, the motion is specifically different, and so cannot really be one, for motion that is one must be specifically one, though motion that is specifically one is not necessarily one in an unqualified sense. We have now explained what we mean when we call a motion one without qualification.
ἔτι δὲ λέγεται μία καὶ ἡ τέλειος, ἐάν τε κατὰ γένος ἐάν τε κατ' εἶδος ᾖ ἐάν τε κατ' οὐσίαν, ὥσπερ καὶ ἐπὶ τῶν ἄλλων τὸ τέλειον καὶ ὅλον τοῦ ἑνός. ἔστι δ' ὅτε κἂν ἀτελὴς ᾖ μία λέγεται, ἐὰν μόνον ᾖ συνεχής.	Further, a motion is also said to be one generically, specifically, or essentially when it is complete, just as in other cases completeness and wholeness are characteristics of what is one: and sometimes a motion even if incomplete is said to be one, provided only that it is continuous.
ἔτι δ' ἄλλως παρὰ τὰς εἰρημένας λέγεται μία κίνησις ἡ ὁμαλής. ἡ γὰρ ἀνώμαλος ἔστιν ὡς οὐ δοκεῖ μία, ἀλλὰ μᾶλλον ἡ ὁμαλής, ὥσπερ ἡ εὐθεῖα· ἡ γὰρ ἀνώμαλος διαιρετή. ἔοικε δὲ διαφέρειν ὡς τὸ μᾶλλον καὶ ἧττον.	And besides the cases already mentioned there is another in which a motion is said to be one, viz. when it is regular: for in a sense a motion that is irregular is not regarded as one, that title belonging rather to that which is regular, as a straight line is regular, the irregular being as such divisible. But the difference would seem to be one of degree.
ἔστιν δὲ ἐν ἁπάσῃ κινήσει τὸ ὁμαλῶς ἢ μή· καὶ γὰρ ἂν ἀλλοιοῖτο ὁμαλῶς, καὶ φέροιτο ἐφ' ὁμαλοῦ οἷον κύκλου ἢ εὐθείας, καὶ περὶ αὔξησιν ὡσαύτως καὶ φθίσιν.	In every kind of motion we may have regularity or irregularity: thus there may be regular alteration, and locomotion in a regular path, e.g. in a circle or on a straight line, and it is the same with regard to increase and decrease.
ἀνωμαλία δ' ἐστὶν διαφορὰ ὁτὲ μὲν ἐφ' ᾧ κινεῖται (ἀδύνατον γὰρ ὁμαλὴν εἶναι τὴν κίνησιν μὴ ἐπὶ ὁμαλῷ μεγέθει, οἷον ἡ τῆς κεκλασμένης κίνησις ἢ ἡ τῆς ἕλικος ἢ ἄλλου μεγέθους, ὧν μὴ ἐφαρμόττει τὸ τυχὸν ἐπὶ τὸ τυχὸν μέρος)· ἡ δὲ οὔτε ἐν τῷ ὃ οὔτ' ἐν τῷ πότε οὔτε ἐν τῷ εἰς ὅ, ἀλλ' ἐν τῷ ὥς. ταχυτῆτι γὰρ καὶ βραδυτῆτι ἐνίοτε διώρισται· ἧς μὲν γὰρ τὸ αὐτὸ τάχος, ὁμαλής, ἧς δὲ μή, ἀνώμαλος.	The difference that makes a motion irregular is sometimes to be found in its path: thus a motion cannot be regular if its path is an irregular magnitude, e.g. a broken line, a spiral, or any other magnitude that is not such that any part of it taken at random fits on to any other that may be chosen. Sometimes it is found neither in the place nor in the time nor in the goal but in the manner of the motion: for in some cases the motion is differentiated by quickness and slowness: thus if its velocity is uniform a motion is regular, if not it is irregular.
διὸ οὐκ εἴδη κινήσεως οὐδὲ διαφοραὶ τάχος καὶ βραδυτής, ὅτι πάσαις ἀκολουθεῖ ταῖς διαφόροις κατ' εἶδος. ὥστε οὐδὲ βαρύτης καὶ κουφότης ἡ εἰς τὸ αὐτό, οἷον γῆς πρὸς αὑτὴν ἢ πυρὸς πρὸς (229a.) αὑτό.	So quickness and slowness are not species of motion nor do they constitute specific differences of motion, because this distinction occurs in connexion with all the distinct species of motion. The same is true of heaviness and lightness when they refer to the same thing: e.g. they do not specifically distinguish earth from itself or fire from itself.
μία μὲν οὖν ἡ ἀνώμαλος τῷ συνεχὴς <�εἶναι>, ἧττον δέ, ὅπερ τῇ κεκλασμένῃ συμβαίνει φορᾷ· τὸ δ' ἧττον μίξις αἰεὶ τοῦ ἐναντίου.	Irregular motion, therefore, while in virtue of being continuous it is one, is so in a lesser degree, as is the case with locomotion in a broken line: and a lesser degree of something always means an admixture of its contrary.
εἰ δὲ πᾶσαν τὴν μίαν ἐνδέχεται καὶ ὁμαλὴν εἶναι καὶ μή, οὐκ ἂν εἴησαν αἱ ἐχόμεναι αἱ μὴ κατ' εἶδος αἱ αὐταὶ μία καὶ συνεχής· πῶς γὰρ ἂν εἴη ὁμαλὴς ἡ ἐξ ἀλλοιώ σεως συγκειμένη καὶ φορᾶς; δέοι γὰρ ἂν ἐφαρμόττειν.	And since every motion that is one can be both regular and irregular, motions that are consecutive but not specifically the same cannot be one and continuous: for how should a motion composed of alteration and locomotion be regular? If a motion is to be regular its parts ought to fit one another.

Lectio 8
Contrariety of motions

Chapter 5
Ἔτι δὲ διοριστέον ποία κίνησις ἐναντία κινήσει, καὶ περὶ μονῆς δὲ τὸν αὐτὸν τρόπον. διαιρετέον δὲ πρῶτον πότερον ἐναντία κίνησις ἡ ἐκ τοῦ αὐτοῦ τῇ εἰς τὸ αὐτό (οἷον ἡ ἐξ ὑγιείας τῇ εἰς ὑγίειαν), οἷον καὶ γένεσις καὶ φθορὰ δοκεῖ, ἢ ἡ ἐξ ἐναντίων (οἷον ἡ ἐξ ὑγιείας τῇ ἐκ νόσου), ἢ ἡ εἰς ἐναντία (οἷον ἡ εἰς ὑγίειαν τῇ εἰς νόσον), ἢ ἡ ἐξ ἐναντίου τῇ εἰς ἐναντίον (οἷον ἡ ἐξ ὑγιείας τῇ εἰς νόσον), ἢ ἡ ἐξ ἐναντίου εἰς ἐναντίον τῇ ἐξ ἐναντίου εἰς ἐναντίον (οἷον ἡ ἐξ ὑγιείας εἰς νόσον τῇ ἐκ νόσου εἰς ὑγίειαν). ἀνάγκη γὰρ ἢ ἕνα τινὰ τούτων εἶναι τῶν τρόπων ἢ πλείους· οὐ γὰρ ἔστιν ἄλλως ἀντιτιθέναι.	We have further to determine what motions are contrary to each other, and to determine similarly how it is with rest. And we have first to decide whether contrary motions are motions respectively from and to the same thing, e.g. a motion from health and a motion to health (where the opposition, it would seem, is of the same kind as that between coming to be and ceasing to be); or motions respectively from contraries, e.g. a motion from health and a motion from disease; or motions respectively to contraries, e.g. a motion to health and a motion to disease; or motions respectively from a contrary and to the opposite contrary, e.g. a motion from health and a motion to disease; or motions respectively from a contrary to the opposite contrary and from the latter to the former, e.g. a motion from health to disease and a motion from disease to health: for motions must be contrary to one another in one or more of these ways, as there is no other way in which they can be opposed.
ἔστι δ' ἡ μὲν ἐξ ἐναντίου τῇ εἰς ἐναντίον οὐκ ἐναντία, οἷον ἡ ἐξ ὑγιείας τῇ εἰς νόσον· ἡ αὐτὴ γὰρ καὶ μία. τὸ μέντοι γ' εἶναι οὐ ταὐτὸ αὐταῖς, ὥσπερ οὐ ταὐτὸ τὸ ἐξ ὑγιείας μεταβάλλειν καὶ τὸ εἰς νόσον.	Now motions respectively from a contrary and to the opposite contrary, e.g. a motion from health and a motion to disease, are not contrary motions: for they are one and the same. (Yet their essence is not the same, just as changing from health is different from changing to disease.)
οὐδ' ἡ ἐξ ἐναντίου τῇ ἐξ ἐναντίου· ἅμα μὲν γὰρ συμβαίνει ἐξ ἐναντίου καὶ εἰς ἐναντίον ἢ μεταξύ—ἀλλὰ περὶ τούτου μὲν ὕστερον ἐροῦμεν,	Nor are motion respectively from a contrary and from the opposite contrary contrary motions, for a motion from a contrary is at the same time a motion to a contrary or to an intermediate (of this, however, we shall speak later),
ἀλλὰ μᾶλλον τὸ εἰς ἐναντίον μεταβάλλειν δόξειεν ἂν εἶναι αἴτιον τῆς ἐναντιώσεως ἢ τὸ ἐξ ἐναντίου· ἡ μὲν γὰρ ἀπαλλαγὴ ἐναντιότητος, ἡ δὲ λῆψις.	but changing to a contrary rather than changing from a contrary would seem to be the cause of the contrariety of motions, the latter being the loss, the former the gain, of contrariness.
καὶ λέγεται δ' ἑκάστη εἰς ὃ μεταβάλλει μᾶλλον ἢ ἐξ οὗ, οἷον ὑγίανσις ἡ εἰς ὑγίειαν, νόσανσις δ' ἡ εἰς νόσον.	Moreover, each several motion takes its name rather from the goal than from the starting-point of change, e.g. motion to health we call convalescence, motion to disease sickening.
λείπεται δὴ ἡ εἰς ἐναντία καὶ ἡ εἰς ἐναντία ἐξ ἐναντίων. τάχα μὲν οὖν συμβαίνει τὰς εἰς ἐναντία καὶ ἐξ ἐναντίων εἶναι, ἀλλὰ τὸ εἶναι ἴσως οὐ ταὐτό, λέγω δὲ τὸ εἰς ὑγίειαν τῷ ἐκ νόσου καὶ τὸ ἐξ ὑγιείας τῷ εἰς νόσον.	Thus we are left with motions respectively to contraries, and motions respectively to contraries from the opposite contraries. Now it would seem that motions to contraries are at the same time motions from contraries (though their essence may not be the same; 'to health' is distinct, I mean, from 'from disease', and 'from health' from 'to disease').
ἔστι δ' ἡ μὲν ἐξ ἐναντίου τῇ εἰς ἐναντίον οὐκ ἐναντία, οἷον ἡ ἐξ ὑγιείας τῇ εἰς νόσον· ἡ αὐτὴ γὰρ καὶ μία. τὸ μέντοι γ' εἶναι οὐ ταὐτὸ αὐταῖς, ὥσπερ οὐ ταὐτὸ τὸ ἐξ ὑγιείας μεταβάλλειν καὶ τὸ εἰς νόσον. οὐδ' ἡ ἐξ ἐναντίου τῇ ἐξ ἐναντίου· ἅμα μὲν γὰρ συμβαίνει ἐξ ἐναντίου καὶ εἰς ἐναντίον ἢ μεταξύ—ἀλλὰ περὶ τούτου μὲν ὕστερον ἐροῦμεν, ἀλλὰ μᾶλλον τὸ εἰς ἐναντίον μεταβάλλειν δόξειεν ἂν εἶναι αἴτιον τῆς ἐναντιώσεως ἢ τὸ ἐξ ἐναντίου· ἡ μὲν γὰρ ἀπαλλαγὴ ἐναντιότητος, ἡ δὲ λῆψις. καὶ λέγεται δ' ἑκάστη εἰς ὃ μεταβάλ λει μᾶλλον ἢ ἐξ οὗ, οἷον ὑγίανσις ἡ εἰς ὑγίειαν, νόσανσις δ' ἡ εἰς νόσον. λείπεται δὴ ἡ εἰς ἐναντία καὶ ἡ εἰς ἐναντία ἐξ ἐναντίων. τάχα μὲν οὖν συμβαίνει τὰς εἰς ἐναντία καὶ ἐξ ἐναντίων εἶναι, ἀλλὰ τὸ εἶναι ἴσως οὐ ταὐτό, λέγω δὲ τὸ εἰς ὑγίειαν τῷ ἐκ νόσου καὶ τὸ ἐξ ὑγιείας τῷ εἰς νόσον.	Now motions respectively from a contrary and to the opposite contrary, e.g. a motion from health and a motion to disease, are not contrary motions: for they are one and the same. (Yet their essence is not the same, just as changing from health is different from changing to disease.) Nor are motion respectively from a contrary and from the opposite contrary contrary motions, for a motion from a contrary is at the same time a motion to a contrary or to an intermediate (of this, however, we shall speak later), but changing to a contrary rather than changing from a contrary would seem to be the cause of the contrariety of motions, the latter being the loss, the former the gain, of contrariness. Moreover, each several motion takes its name rather from the goal than from the starting-point of change, e.g. motion to health we call convalescence, motion to disease sickening. Thus we are left with motions respectively to contraries, and motions respectively to contraries from the opposite contraries. Now it would seem that motions to contraries are at the same time motions from contraries (though their essence may not be the same; 'to health' is distinct, I mean, from 'from disease', and 'from health' from 'to disease').
ἐπεὶ δὲ διαφέρει μεταβολὴ κινήσεως (ἡ ἔκ τινος γὰρ ὑποκειμένου εἴς τι ὑποκείμενον μεταβολὴ κίνησίς ἐστιν), ἡ ἐξ ἐναντίου (229b.) εἰς ἐναντίον τῇ ἐξ ἐναντίου εἰς ἐναντίον κίνησις ἐναντία, οἷον ἡ ἐξ ὑγιείας εἰς νόσον τῇ ἐκ νόσου εἰς ὑγίειαν.	Since then change differs from motion (motion being change from a particular subject to a particular subject), it follows that contrary motions are motions respectively from a contrary to the opposite contrary and from the latter to the former, e.g. a motion from health to disease and a motion from disease to health.
δῆλον δὲ καὶ ἐκ τῆς ἐπαγωγῆς ὁποῖα δοκεῖ τὰ ἐναντία εἶναι· τὸ νοσάζεσθαι γὰρ τῷ ὑγιάζεσθαι καὶ τὸ μανθάνειν τῷ ἀπατᾶσθαι μὴ δι' αὑτοῦ (εἰς ἐναντία γάρ· ὥσπερ γὰρ ἐπιστήμην, ἔστι καὶ ἀπάτην καὶ δι' αὑτοῦ κτᾶσθαι καὶ δι' ἄλλου), καὶ ἡ ἄνω φορὰ τῇ κάτω (ἐναντία γὰρ ταῦτα ἐν μήκει), καὶ ἡ εἰς δεξιὰ τῇ εἰς ἀριστερά (ἐναντία γὰρ ταῦτα ἐν πλάτει), καὶ ἡ εἰς τὸ ἔμπροσθεν τῇ εἰς τὸ ὄπισθεν (ἐναντία γὰρ καὶ ταῦτα).	Moreover, the consideration of particular examples will also show what kinds of processes are generally recognized as contrary: thus falling ill is regarded as contrary to recovering one's health, these processes having contrary goals, and being taught as contrary to being led into error by another, it being possible to acquire error, like knowledge, either by one's own agency or by that of another. Similarly we have upward locomotion and downward locomotion, which are contrary lengthwise, locomotion to the right and locomotion to the left, which are contrary breadthwise, and forward locomotion and backward locomotion, which too are contraries.
ἡ δ' εἰς ἐναντίον μόνον οὐ κίνησις ἀλλὰ μεταβολή, οἷον τὸ γίγνεσθαι λευκὸν μὴ ἔκ τινος.	On the other hand, a process simply to a contrary, e.g. that denoted by the expression 'becoming white', where no starting-point is specified, is a change but not a motion.
καὶ ὅσοις δὲ μὴ ἔστιν ἐναντία, ἡ ἐξ αὐτοῦ τῇ εἰς αὐτὸ μεταβολῇ ἐναντία· διὸ γένεσις φθορᾷ ἐναντία καὶ ἀποβολὴ λήψει· αὗται δὲ μεταβολαὶ μέν, κινήσεις δ' οὔ.	And in all cases of a thing that has no contrary we have as contraries change from and change to the same thing. Thus coming to be is contrary to ceasing to be, and losing to gaining. But these are changes and not motions.
τὰς δ' εἰς τὸ μεταξὺ κινήσεις, ὅσοις τῶν ἐναντίων ἔστι μεταξύ, ὡς εἰς ἐναντία πως θετέον· ὡς ἐναντίῳ γὰρ χρῆται τῷ μεταξὺ ἡ κίνησις, ἐφ' ὁπότερα ἂν μεταβάλλῃ, οἷον ἐκ φαιοῦ μὲν εἰς τὸ λευκὸν ὡς ἐκ μέλανος, καὶ ἐκ λευκοῦ εἰς φαιὸν ὡς εἰς μέλαν, ἐκ δὲ μέλανος εἰς φαιὸν ὡς εἰς λευκὸν τὸ φαιόν· τὸ γὰρ μέσον πρὸς ἑκάτερον λέγεταί πως ἑκάτερον τῶν ἄκρων, καθάπερ εἴρηται καὶ πρότερον. κίνησις μὲν δὴ κινήσει ἐναντία οὕτως ἡ ἐξ ἐναντίου εἰς ἐναντίον τῇ ἐξ ἐναντίου εἰς ἐναντίον.	And wherever a pair of contraries admit of an intermediate, motions to that intermediate must be held to be in a sense motions to one or other of the contraries: for the intermediate serves as a contrary for the purposes of the motion, in whichever direction the change may be, e.g. grey in a motion from grey to white takes the place of black as starting-point, in a motion from white to grey it takes the place of black as goal, and in a motion from black to grey it takes the place of white as goal: for the middle is opposed in a sense to either of the extremes, as has been said above. Thus we see that two motions are contrary to each other only when one is a motion from a contrary to the opposite contrary and the other is a motion from the latter to the former.

Lectio 9
Contrariety of rest to motion, and of rest to rest

Chapter 6
6 Ἐπεὶ δὲ κινήσει οὐ μόνον δοκεῖ κίνησις εἶναι ἐναντία ἀλλὰ καὶ ἠρεμία, τοῦτο διοριστέον. ἁπλῶς μὲν γὰρ ἐναντίον κίνησις κινήσει, ἀντίκειται δὲ καὶ ἠρεμία (στέρησις γάρ, ἔστι δ' ὡς καὶ ἡ στέρησις ἐναντία λέγεται),	But since a motion appears to have contrary to it not only another motion but also a state of rest, we must determine how this is so. A motion has for its contrary in the strict sense of the term another motion, but it also has for an opposite a state of rest (for rest is the privation of motion and the privation of anything may be called its contrary),
ποιᾷ δὲ ποιά, οἷον τῇ κατὰ τόπον ἡ κατὰ τόπον. ἀλλὰ τοῦτο νῦν λέγεται ἁπλῶς· πότερον γὰρ τῇ ἐνταῦθα μονῇ ἡ ἐκ τούτου ἢ ἡ εἰς τοῦτο κίνησις ἀντίκειται;	and motion of one kind has for its opposite rest of that kind, e.g. local motion has local rest. This statement, however, needs further qualification: there remains the question, is the opposite of remaining at a particular place motion from or motion to that place?
δῆλον δὴ ὅτι, ἐπεὶ ἐν δυσὶν ἡ κίνησις ὑποκειμένοις, τῇ μὲν ἐκ τούτου εἰς τὸ ἐναντίον ἡ ἐν τούτῳ μονή, τῇ δ' ἐκ τοῦ ἐναντίου εἰς τοῦτο ἡ ἐν τῷ ἐναντίῳ.	It is surely clear that since there are two subjects between which motion takes place, motion from one of these (A) to its contrary (B) has for its opposite remaining in A while the reverse motion has for its opposite remaining in B.
ἅμα δὲ καὶ ἀλλήλαις ἐναντίαι αὗται· καὶ γὰρ ἄτοπον, εἰ κινήσεις (230a.) μὲν ἐναντίαι εἰσίν, ἠρεμίαι δ' ἀντικείμεναι οὐκ εἰσίν. εἰσὶν δὲ αἱ ἐν τοῖς ἐναντίοις, οἷον ἡ ἐν ὑγιείᾳ τῇ ἐν νόσῳ ἠρεμίᾳ	At the same time these two are also contrary to each other: for it would be absurd to suppose that there are contrary motions and not opposite states of rest. States of rest in contraries are opposed. To take an example, a state of rest in health is (1) contrary to a state of rest in disease,
(κινήσει δὲ τῇ ἐξ ὑγιείας εἰς νόσον· τῇ γὰρ ἐκ νόσου εἰς ὑγίειαν ἄλογον—ἡ γὰρ εἰς αὐτὸ κίνησις ἐν ᾧ ἕστηκεν, ἠρέμησις μᾶλλόν ἐστιν, ἢ συμβαίνει γε ἅμα γίγνεσθαι τῇ κινήσει ἀνάγκη δὲ ἢ ταύτην ἢ ἐκείνην εἶναι)· οὐ γὰρ ἥ γ' ἐν λευκότητι ἠρεμία ἐναντία τῇ ἐν ὑγιείᾳ.	and (2) the motion to which it is contrary is that from health to disease. For (2) it would be absurd that its contrary motion should be that from disease to health, since motion to that in which a thing is at rest is rather a coming to rest, the coming to rest being found to come into being simultaneously with the motion; and one of these two motions it must be. And (1) rest in whiteness is of course not contrary to rest in health.
ὅσοις δὲ μὴ ἔστιν ἐναντία, τούτων μεταβολὴ μέν ἐστιν ἀντικειμένη ἡ ἐξ αὐτοῦ τῇ εἰς αὐτό, κίνησις δ' οὐκ ἔστιν,	Of all things that have no contraries there are opposite changes (viz. change from the thing and change to the thing, e.g. change from being and change to being), but no motion.
οἷον ἡ ἐξ ὄντος τῇ εἰς ὄν, καὶ μονὴ μὲν τούτων οὐκ ἔστιν, ἀμεταβλησία δέ.	So, too, of such things there is no remaining though there is absence of change.
καὶ εἰ μέν τι εἴη ὑποκείμενον, ἡ ἐν τῷ ὄντι ἀμεταβλησία τῇ ἐν τῷ μὴ ὄντι ἐναντία. εἰ δὲ μὴ ἔστι τι τὸ μὴ ὄν, ἀπορήσειεν ἄν τις τίνι ἐναντία ἡ ἐν τῷ ὄντι ἀμεταβλησία, καὶ εἰ ἠρεμία ἐστίν.	Should there be a particular subject, absence of change in its being will be contrary to absence of change in its not-being. And here a difficulty may be raised: if not-being is not a particular something, what is it, it may be asked, that is contrary to absence of change in a thing's being? and is this absence of change a state of rest?
εἰ δὲ τοῦτο, ἢ οὐ πᾶσα ἠρεμία κινήσει ἐναντία, ἢ ἡ γένεσις καὶ φθορὰ κίνησις. δῆλον τοίνυν ὅτι ἠρεμία μὲν οὐ λεκτέα, εἰ μὴ καὶ αὗται κινήσεις,	If it is, then either it is not true that every state of rest is contrary to a motion or else coming to be and ceasing to be are motion. It is clear then that, since we exclude these from among motions, we must not say that this absence of change is a state of rest:
ὅμοιον δέ τι καὶ ἀμεταβλησία· ἐναντία δὲ ἢ οὐδενὶ ἢ τῇ ἐν τῷ μὴ ὄντι ἢ τῇ φθορᾷ· αὕτη γὰρ ἐξ αὐτῆς, ἡ δὲ γένεσις εἰς ἐκείνην.	we must say that it is similar to a state of rest and call it absence of change. And it will have for its contrary either nothing or absence of change in the thing's not-being, or the ceasing to be of the thing: for such ceasing to be is change from it and the thing's coming to be is change to it.

Lectio 10
Certain difficulties are resolved

Chapter 6 cont.
ἀπορήσειε δ' ἄν τις διὰ τί ἐν μὲν τῇ κατὰ τόπον μεταβολῇ εἰσὶ καὶ κατὰ φύσιν καὶ παρὰ φύσιν καὶ μοναὶ καὶ κινήσεις, ἐν δὲ ταῖς ἄλλαις οὔ, οἷον ἀλλοίωσις ἡ μὲν κατὰ φύσιν ἡ δὲ παρὰ φύσιν (οὐδὲν γὰρ μᾶλλον ἡ ὑγίανσις ἢ ἡ νόσανσις κατὰ φύσιν ἢ παρὰ φύσιν, οὐδὲ λεύκανσις ἢ μέλανσις)· ὁμοίως δὲ καὶ ἐπ' αὐξήσεως καὶ φθίσεως (οὔτε γὰρ αὗται ἀλλήλαις ἐναντίαι ὡς φύσει ἡ δὲ παρὰ φύσιν, οὔτ' αὔξησις αὐξή σει)· καὶ ἐπὶ γενέσεως δὲ καὶ φθορᾶς ὁ αὐτὸς λόγος· οὔτε γὰρ ἡ μὲν γένεσις κατὰ φύσιν ἡ δὲ φθορὰ παρὰ φύσιν (τὸ γὰρ γηρᾶν κατὰ φύσιν), οὔτε γένεσιν ὁρῶμεν τὴν μὲν κατὰ φύσιν τὴν δὲ παρὰ φύσιν.	Again, a further difficulty may be raised. How is it, it may be asked, that whereas in local change both remaining and moving may be natural or unnatural, in the other changes this is not so? e.g. alteration is not now natural and now unnatural, for convalescence is no more natural or unnatural than falling ill, whitening no more natural or unnatural than blackening; so, too, with increase and decrease: these are not contrary to each other in the sense that either of them is natural while the other is unnatural, nor is one increase contrary to another in this sense; and the same account may be given of becoming and perishing: it is not true that becoming is natural and perishing unnatural (for growing old is natural), nor do we observe one becoming to be natural and another unnatural.
ἢ εἰ ἔστιν τὸ βίᾳ παρὰ φύσιν, καὶ φθορὰ ἂν εἴη φθορᾷ ἐναντία ἡ βίαιος ὡς παρὰ φύσιν οὖσα τῇ κατὰ φύσιν; ἆρ' οὖν καὶ γενέσεις εἰσὶν ἔνιαι βίαιοι καὶ οὐχ εἱμαρμέναι, αἷς ἐναντίαι αἱ κατὰ φύσιν, (230b.) καὶ αὐξήσεις βίαιοι καὶ φθίσεις, οἷον αὐξήσεις αἱ τῶν ταχὺ διὰ τρυφὴν ἡβώντων, καὶ οἱ σῖτοι οἱ ταχὺ ἁδρυνόμενοι καὶ μὴ πιληθέντες; ἐπὶ δ' ἀλλοιώσεως πῶς; ἢ ὡσαύτως; εἶεν γὰρ ἄν τινες βίαιοι, αἱ δὲ φυσικαί, οἷον οἱ ἀφιέμενοι μὴ ἐν κρισίμοις ἡμέραις, οἱ δ' ἐν κρισίμοις· οἱ μὲν οὖν παρὰ φύσιν ἠλλοίωνται, οἱ δὲ κατὰ φύσιν.	We answer that if what happens under violence is unnatural, then violent perishing is unnatural and as such contrary to natural perishing. Are there then also some becomings that are violent and not the result of natural necessity, and are therefore contrary to natural becomings, and violent increases and decreases, e.g. the rapid growth to maturity of profligates and the rapid ripening of seeds even when not packed close in the earth? And how is it with alterations? Surely just the same: we may say that some alterations are violent while others are natural, e.g. patients alter naturally or unnaturally according as they throw off fevers on the critical days or not.
ἔσονται δὴ καὶ φθοραὶ ἐναντίαι ἀλλήλαις, οὐ γενέσεσι. καὶ τί γε κωλύει ἔστιν ὡς; καὶ γὰρ εἰ ἡ μὲν ἡδεῖα ἡ δὲ λυπηρὰ εἴη· ὥστε οὐχ ἁπλῶς φθορὰ φθορᾷ ἐναντία, ἀλλ' ᾗ ἡ μὲν τοιαδὶ ἡ δὲ τοιαδὶ αὐτῶν ἐστιν.	But, it may be objected, then we shall have perishings contrary to one another, not to becoming. Certainly: and why should not this in a sense be so? Thus it is so if one perishing is pleasant and another painful: and so one perishing will be contrary to another not in an unqualified sense, but in so far as one has this quality and the other that.
ὅλως μὲν οὖν ἐναντίαι κινήσεις καὶ ἠρεμίαι τὸν εἰρημένον τρόπον εἰσίν, οἷον ἡ ἄνω τῇ κάτω· τόπου γὰρ ἐναντιώσεις αὗται. φέρεται δὲ τὴν μὲν ἄνω φορὰν φύσει τὸ πῦρ, τὴν δὲ κάτω ἡ γῆ· καὶ ἐναντίαι γ' αὐτῶν αἱ φοραί. τὸ δὲ πῦρ ἄνω μὲν φύσει, κάτω δὲ παρὰ φύσιν· καὶ ἐναντία γε ἡ κατὰ φύσιν αὐτοῦ τῇ παρὰ φύσιν. καὶ μοναὶ δ' ὡσαύτως· ἡ γὰρ ἄνω μονὴ τῇ ἄνωθεν κάτω κινήσει ἐναντία. γίγνεται δὲ τῇ γῇ ἡ μὲν μονὴ ἐκείνη παρὰ φύσιν, ἡ δὲ κίνησις αὕτη κατὰ φύσιν. ὥστε κινήσει μονὴ ἐναντία ἡ παρὰ φύσιν τῇ κατὰ φύσιν τοῦ αὐτοῦ· καὶ γὰρ ἡ κίνησις ἡ τοῦ αὐτοῦ ἐναντία οὕτως· ἡ μὲν γὰρ κατὰ φύσιν [ἔσται] αὐτῶν, ἡ ἄνω ἢ ἡ κάτω, ἡ δὲ παρὰ φύσιν.	Now motions and states of rest universally exhibit contrariety in the manner described above, e.g. upward motion and rest above are respectively contrary to downward motion and rest below, these being instances of local contrariety; and upward locomotion belongs naturally to fire and downward to earth, i.e. the locomotions of the two are contrary to each other. And again, fire moves up naturally and down unnaturally: and its natural motion is certainly contrary to its unnatural motion. Similarly with remaining: remaining above is contrary to motion from above downwards, and to earth this remaining comes unnaturally, this motion naturally. So the unnatural remaining of a thing is contrary to its natural motion, just as we find a similar contrariety in the motion of the same thing: one of its motions, the upward or the downward, will be natural, the other unnatural.
ἔχει δ' ἀπορίαν εἰ ἔστιν πάσης ἠρεμίας τῆς μὴ αἰεὶ γένεσις, καὶ αὕτη τὸ ἵστασθαι. τοῦ δὴ παρὰ φύσιν μένοντος, οἷον τῆς γῆς ἄνω, εἴη ἂν γένεσις. ὅτε ἄρα ἐφέρετο ἄνω βίᾳ, ἵστατο. ἀλλὰ τὸ ἱστάμενον ἀεὶ δοκεῖ φέρεσθαι θᾶττον, τὸ δὲ βίᾳ τοὐναντίον. οὐ γενόμενον ἄρα ἠρεμοῦν ἔσται ἠρεμοῦν.	Here, however, the question arises, has every state of rest that is not permanent a becoming, and is this becoming a coming to a standstill? If so, there must be a becoming of that which is at rest unnaturally, e.g. of earth at rest above: and therefore this earth during the time that it was being carried violently upward was coming to a standstill. But whereas the velocity of that which comes to a standstill seems always to increase, the velocity of that which is carried violently seems always to decrease: so it will he in a state of rest without having become so.
ἔτι δοκεῖ τὸ ἵστασθαι ἢ ὅλως εἶναι τὸ εἰς τὸν αὑτοῦ τόπον φέρεσθαι ἢ συμβαίνειν ἅμα.	Moreover 'coming to a standstill' is generally recognized to be identical or at least concomitant with the locomotion of a thing to its proper place.
ἔχει δ' ἀπορίαν εἰ ἐναντία ἡ μονὴ ἡ ἐνταῦθα τῇ ἐντεῦθεν κινήσει· ὅταν γὰρ κινῆται ἐκ τουδὶ καὶ ἀποβάλλῃ, ἔτι δοκεῖ ἔχειν τὸ ἀποβαλλόμενον, ὥστ' εἰ αὕτη ἡ ἠρεμία ἐναντία τῇ ἐντεῦθεν εἰς τοὐναντίον κινήσει, ἅμα ὑπάρξει τἀναντία.	There is also another difficulty involved in the view that remaining in a particular place is contrary to motion from that place. For when a thing is moving from or discarding something, it still appears to have that which is being discarded, so that if a state of rest is itself contrary to the motion from the state of rest to its contrary, the contraries rest and motion will be simultaneously predicable of the same thing.
ἢ πῂ ἠρεμεῖ, εἰ ἔτι μένει, ὅλως δὲ τοῦ κινουμένου τὸ μὲν (231a.) ἐκεῖ, τὸ δ' εἰς ὃ μεταβάλλει; διὸ καὶ μᾶλλον κίνησις κινήσει ἐναντίον ἢ ἠρέμησις. καὶ περὶ μὲν κινήσεως καὶ ἠρεμίας, πῶς ἑκατέρα μία, καὶ τίνες ἐναντίαι τίσιν, εἴρηται.	May we not say, however, that in so far as the thing is still stationary it is in a state of rest in a qualified sense? For, in fact, whenever a thing is in motion, part of it is at the starting-point while part is at the goal to which it is changing: and consequently a motion finds its true contrary rather in another motion than in a state of rest. With regard to motion and rest, then, we have now explained in what sense each of them is one and under what conditions they exhibit contrariety.
[ἀπορήσειε δ' ἄν τις καὶ περὶ τοῦ ἵστασθαι, εἰ καὶ ὅσαι παρὰ φύσιν κινήσεις, ταύταις ἔστιν ἠρεμία ἀντικειμένη. εἰ μὲν οὖν μὴ ἔσται, ἄτοπον· μένει γάρ, βίᾳ δέ. ὥστε ἠρεμοῦν τι ἔσται οὐκ ἀεὶ ἄνευ τοῦ γενέσθαι. ἀλλὰ δῆλον ὅτι ἔσται· ὥσπερ γὰρ κινεῖται παρὰ φύσιν, καὶ ἠρεμοίη ἄν τι παρὰ φύσιν.	[With regard to coming to a standstill the question may be raised whether there is an opposite state of rest to unnatural as well as to natural motions. It would be absurd if this were not the case: for a thing may remain still merely under violence: thus we shall have a thing being in a non-permanent state of rest without having become so. But it is clear that it must be the case: for just as there is unnatural motion, so, too, a thing may be in an unnatural state of rest.
ἐπεὶ δ' ἔστιν ἐνίοις κίνησις κατὰ φύσιν καὶ παρὰ φύσιν, οἷον πυρὶ ἡ ἄνω κατὰ φύσιν ἡ δὲ κάτω παρὰ φύσιν, πότερον αὕτη ἐναντία ἢ ἡ τῆς γῆς; αὕτη γὰρ φέρεται κατὰ φύσιν κάτω. ἢ δῆλον ὅτι ἄμφω, ἀλλ' οὐχ ὡσαύτως, ἀλλ' ἡ μὲν κατὰ φύσιν ὡς κατὰ φύσιν οὔσης τῆς αὐτοῦ· ἡ δ' ἄνω τοῦ πυρὸς τῇ κάτω, ὡς ἡ κατὰ φύσιν οὖσα τῇ παρὰ φύσιν οὔσῃ. ὁμοίως δὲ καὶ ταῖς μοναῖς.	Further, some things have a natural and an unnatural motion, e.g. fire has a natural upward motion and an unnatural downward motion: is it, then, this unnatural downward motion or is it the natural downward motion of earth that is contrary to the natural upward motion? Surely it is clear that both are contrary to it though not in the same sense: the natural motion of earth is contrary inasmuch as the motion of fire is also natural, whereas the upward motion of fire as being natural is contrary to the downward motion of fire as being unnatural. The same is true of the corresponding cases of remaining.
ἴσως δ' ἠρεμίᾳ κίνησίς πῃ ἀντίκειται.] Cum enim moveatur ex hoc et abiciat, adhuc videtur habere qod abiicitur. Quare si ipsa quies contraria[t] ei qui hinc est in contrarium motui, simul existunt contraria, si aliquatenus quiescit aut adhuc manet. Totaliter autem ei quod movetur, hoc quidem ibi, hoc autem in quod mutatur. Propter quod magis motui contrarium, quam quies. Quis quidem igitur motus simpliciter unus, dictum est; et de motu quidem et quiete, quomodo uterque unus, et qui contrarii quibus, dictum est.	But there would seem to be a sense in which a state of rest and a motion are opposites.] For, since it is moved from this and casts it off, it seems still to have what is cast off. So, if the very rest is contrary to that which is thus in opposition to motion, two contraries will exist simultaneously—if it rests a little, or still remains. In general, what is in motion [is opposed] by being here and by what it is being changed into. Therefore contrary motion is more opposed to motion than rest. Which motion is simply one, has been said, and likewise how motion and rest are each one, and what is contrary to what.