§7.4#2ἀλλʼ ἄρα οὐ μόνον
δεῖ τὰ συμβλητὰ μὴ ὁμώνυμα εἶναι ἀλλὰ καὶ μὴ ἔχειν διαφοράν, μήτε ὃ μήτε ἐν ᾧ;
But, then, is it not only necessary for comparable things not to be homonymous, but also to have no difference, neither in what they are nor in that in which they are?
λέγω δὲ οἷον χρῶμα ἔχει διαίρεσιν· τοιγαροῦν οὐ συμβλητὸν κατὰ τοῦτο (οἷον πότερον κεχρωμάτισται μᾶλλον, μὴ κατὰ τὶ χρῶμα, ἀλλʼ ᾗ χρῶμα) ἀλλὰ κατὰ τὸ λευκόν.
I mean, for example, color has a division; therefore, it is not comparable in this respect (for example, whether a thing is more colored, not in respect of some particular color, but qua color), but in respect of white.
οὕτω καὶ περὶ κίνησιν ὁμοταχὲς τῷ ἐν ἴσῳ χρόνῳ κινεῖσθαι ἴσον τοσονδί·
So too with motion: equal velocity consists in moving an equal, specific amount in an equal time.
εἰ δὴ τοῦ μήκους ἐν τῳδὶ τὸ μὲν ἠλλοιώθη τὸ δʼ νέχθη, ἴση ἄρα αὕτη ἡ ἀλλοίωσις καὶ ὁμοταχὴς τὴ φορᾷ;
If indeed, in this time, one thing has been altered in respect of length and another has undergone locomotion, is this alteration then equal and of equal velocity to the locomotion?
ἀλλʼ ἄτοπον.
But this is absurd.
αἴτιον δʼ ὅτι ἡ κίνησις ἔχει εἴδη, ὥστʼ εἰ τὰ ἐν ἴσῳ χρόνῳ ἐνεχθέντα ἴσον μῆκος ἰσοταχῆ ἔσται, ἴση ἡ εὐθεῖα καὶ ἡ περιφερής.
The reason is that motion has species, so that if things that have undergone locomotion in an equal time over an equal length are to be of equal velocity, a straight line and a circular line will be equal.
πότερον οὖν αἴτίον, ὅτι ἡ φορὰ γένος ἢ ὅτι ἡ γραμμὴ γένος;
Which then is the cause, that locomotion is a genus or that the line is a genus?
ὁ μὲν γὰρ χρόνος ὁ αὐτός, ἂν δὲ τῷ εἴδει ἦ ἄλλα, καὶ ἐκεῖνα εἴδει διαφέρει.
For the time indeed is the same, but if the things are other in species, those motions also differ in species.
καὶ γὰρ ἡ φορὰ εἴδη ἔχει, ἂν ἐκεῖνο ἔχῃ εἴδη ἐφʼ οὗ κινεῖται (ὁτὲ δὲ ἐὰν ᾧ, οἷον εἰ πόδες, βάδισις, εἰ δὲ πτέρυγες, πτῆσις. ἢ οὔ, ἀλλὰ τοῖς σχήμασιν ἡ φορὰ ἄλλη; ).
For locomotion too has species, if that on which the motion takes place has species (and sometimes if that by which, as if it is feet, walking, but if wings, flight; or not, but locomotion is different according to the figures?).
ὥστε τὰ ἐν ἴσῳ ταὐτὸ μέγεθος κινούμενα ἰσοταχῆ, τὸ αὐτὸ δὲ καὶ ἀδιάφορον εἴδει καὶ κινήσει ἀδιάφορον· ὥστε τοῦτο σκεπτέον, τίς διαφορὰ κινήσεαως.
Thus things that move the same magnitude in an equal time are of equal velocity, and what is the same and indistinguishable in species is also indistinguishable in motion; therefore, this must be investigated: what is the difference of motion.
καὶ σημαίνει ὁ λόγος οὗτος ὅτι τὸ γένος οὐχ ἕν τι, ἀλλὰ παρὰ τοῦτο λανθάνει πολλά, εἰσίν τε τῶν ὁμωνυμιῶν αἱ μὲν πολὺ ἀπέχουσαι, αἱ δὲ ἔχουσαί τινα ὀμοιότητα, αἱ δʼ ἐγγὺς ἢ γένει ἢ ἀναλογίᾳ, διὸ οὐ δοκοῦσιν ὁμωνυμίαι εἶναι οὔσαι.
And this argument signifies that the genus is not some single thing, but because of this many things remain hidden, and among homonyms, some are far apart, others have some similarity, and others are close either by genus or by analogy, wherefore they do not seem to be homonyms although they are.
πότε οὖν ἕτερον τὸ εἶδος, ἐὰν ταὐτὸ ἐν ἄλλῳ, ἢ ἂν ἄλλο ἐν ἄλλῳ;
When then is the species different, if the same is in another, or if another is in another?
καὶ τίς ὅρος;
And what is the definition?
ἢ τῷ κρινοῦμεν ὅτι ταὐτὸν τὸ λευκὸν καὶ τὸ γλυκὺ ἢ ἄλλο—ὅτι ἐν ἄλλῳ φαίνεται ἕτερον, ἢ ὅτι ὅλως οὐ ταὐτό;
Or by what shall we judge that white and sweet are the same or different—is it because they appear different in another, or because they are not the same at all?
περὶ δὲ δὴ ἀλλοιώσεως, πῶς ἔσται ἰσσταχὴς
ἑτέρᾳ ἑτέρα;
But concerning alteration, how will one alteration be of equal velocity to another?
εἰ δή ἐστι τὸ ὑγιάζεσθαι ἀλλοιοῦσθαι, ἔστι τὸν μὲν ταχὺ τὸν δὲ βραδέως ἰαθῆναι, καὶ ἅμα τινάς, ὥστʼ ἔσται ἀλλοίωσις ἰσοταχής· ἐν ἴσῳ γὰρ χρόνῳ ἠλλοιώθη.
If indeed to be healed is to be altered, it is possible for one to be cured quickly and another slowly, and some at the same time, so that there will be equal velocity of alteration; for they were altered in an equal time.
ἀλλὰ τί ἠλλοιώθη;
But what was altered?
τὸ γὰρ ἴσον οὐκ ἔστιν ἐνταῦθα λεγόμενον, ἀλλʼ ὡς ἐν τῷ ποσῷ ἰσότης, ἐνταῦθα ὁμοιότης.
For 'equal' is not the term used here, but as equality is in quantity, so here is likeness.
ἀλλʼ ἔστω ἰσοταχὲς τὸ ἐν ἴσῳ χρόνῳ τὸ αὐτὸ μεταβάλλον.
But let equal velocity be the changing of the same thing in an equal time.
πότερον οὖν ἐν τὸ πάθος ἢ τὸ πάθος δεῖ συμβάλλειν;
Is it then in that in which the affection is, or the affection itself, that we must compare?
ἐνταῦθα μὲν δὴ ὅτι ὑγίεια ἡ αὐτή, ἔστιν λαβεῖν ὅτι οὔτε μᾶλλον οὔτε ἧττον ἀλλʼ ὁμοίως ὑπάρχει.
Here indeed, because the health is the same, we can grasp that it is present neither more nor less, but similarly.
ἐὰν δὲ τὸ πάθος ἄλλο ᾖ, οἷον ἀλλοιοῦται τὸ λευκαινόμενον καὶ τὸ ὑγιαζόμενον, τούτοις οὐδὲν τὸ αὐτὸ οὐδʼ ἴσον οὐδʼ ὅμοιον, ᾗ ἤδη ταῦτα εἴδη ποιεῖ ἀλλοιώσεως, καὶ οὐκ ἔστι μία ὥσπερ οὐδʼ αἱ φοραί.
But if the affection is other, as when that which is being whitened and that which is being healed are altered, in these there is nothing the same, nor equal, nor like, insofar as these already make species of alteration, and it is not one, just as locomotions are not.
ὥστε ληπτέον πόσα εἴδη ἀλλοιώσεως καὶ πόσα φορᾶς.
Thus we must grasp how many species of alteration there are, and how many of locomotion.
εἰ μὲν οὖν τὰ κινούμενα εἴδει διαφέρει, ὧν εἰσὶν αἱ κινήσεις καθʼ αὑτὰ καὶ μὴ κατὰ συμβεβηκός, καὶ αἱ κινήσεις εἴδει διοίσουσιν· εἰ δὲ γένει, γένει, εἰ δʼ ἀριθμῷ, ἀριθμῷ.
If indeed, then, the things that move differ in species, of which the motions belong in themselves and not accidentally, the motions also will differ in species; and if in genus, in genus, and if in number, in number.
ἀλλὰ δὴ πότερον εἰς τὸ πάθος δεῖ βλέψαι, ἐὰν τὸ αὐτὸ ἢ ὅμοιμον, εἰ ἰσοταχεῖς αἱ ἀλλοιώσεις, ἢ εἰς τὸ ἀλλοιούμενον, οἷον εἰ τοῦ μὲν τοσονδὶ λελεύκανται τοῦ δὲ τοσονδί;
But indeed, must we look to the affection, whether it is the same or like, if the alterations are of equal velocity, or to that which is being altered, for instance if so much of one has been whitened and so much of the other?
ἢ εἰς ἄμφω, καὶ ἡ αὐτὴ μὲν ἢ ἄλλη τῷ πάθει, εἰ τὸ αὐτὸ ἢ μὴ τὸ αὐτό, ἴση δʼ ἢ ἄνισος, εἰ ἐκεῖνοἴσον ἢ ἄνισον;
Or to both, and the alteration is the same or other by the affection, if it is the same or not the same, and equal or unequal, if that is equal or unequal?
καὶ ἐπὶ γενέσεως δὲ καὶ φθορᾶς τὸ αὐτὸ σκεπτέον.
And also in the case of generation and destruction, we must consider the same.
πῶς ἰσοταχὴς ἡ γένεσις;
How is generation of equal velocity?
εἰ ἐν ἴσῳ χρόνῳ τὸ αὐτὸ καὶ ἄτομον, οἷον ἄνθρωπος ἀλλὰ μὴ ζῶον· θάτ. τῶν δʼ, εἰ ἐν ἴσῳ ἕτερον (οὐ γὰρ ἔχομέν τινα δύο ἐν οἷς ἡ ἑτερότης ὡς ἡ ἀνομοιότης), ἢ, εἰ ἔστιν ἀριθμὸς ἡ οὐσία, πλείων καὶ ἐλάττων ἀριθμὸς ὁμοειδής· ἀλλʼ ἀνώνυμον τὸ κοινόν, καὶ τὸ ἑκάτερον, ὥσπερ τὸ πλεῖον πάθος ἢ τὸ ὑπερέχον μᾶλλον, τὸ δὲ ποσὸν μεῖζον.
If in an equal time the same and indivisible thing is generated, as a man but not an animal; and faster, if in an equal time another is generated (for we do not have any two things in which the difference is as unlikeness), or, if substance is number, a greater and lesser number of the same species; but the common term has no name, nor does either of the two, just as we speak of a greater affection or that which exceeds more, but in quantity of a larger amount.