§7.4#1Ἀπορήσειε δʼ ἄν τις πότερόν ἐστι κίνησις πᾶσα πάση συμβλητὴ ἢ οὔ.
One might raise the question whether every motion is comparable with every other, or not.
εἰ δή ἐστιν πᾶσα συμβλητή, καὶ μοταχὲς τὸ ἐν ἴσῳ χρόνῳ ἴσον κινούμενον, ἔσται περιφερής τις ἴση εὐθείᾳ, καὶ μείζων δὴ καὶ ἐλάττων.
If indeed all are comparable, and that which moves an equal amount in an equal time is of equal velocity, then some circular line will be equal to a straight line, and indeed also greater and less.
ἔτι ἀλλοίωσις καὶ φορά τις ἴση, ὅταν ἐν ἴσῳ χρόνῳ τὸ μὲν ἀλλοιωθῇ τὸ δʼ ἐνεχθῇ.
Furthermore, some alteration and some locomotion will be equal, when in an equal time one is altered and the other is moved.
ἔσται ἄρα ἴσον πάθος μήκει.
Therefore, an affection (of alteration) will be equal to a length (of locomotion).
ἀλλʼ ἀδύνατον.
But this is impossible.
ἀλλʼ ἄρα ὅταν ἐν ἴσῳ ἴσον κινηθῇ, τότε ἰσοταχές, ἴσον δʼ οὐκ ἔστιν πάθος μήκει, ὥστε οὐκ ἔστιν ἀλλοίωσις φορή ἴση οὐδʼ ἐλάττων, ὥστʼ οὐ πᾶσα συμβλητή;
But then, when there is equal motion in an equal time, only then is there equal velocity, and since an affection is not equal to a length, so alteration is neither equal to nor less than locomotion, so that not every motion is comparable?
ἐπὶ δὲ τοῦ κύκλου
καὶ τῆς εὐθείας πῶς συμβήσεται;
But in the case of the circle and the straight line, how will this turn out?
ἄτοπόν τε γὰρ εἰ μὴ ἔστιν κύκλῳ ὁμοίως τουτὶ κινεῖσθαι καὶ τουτὶ ἐπὶ τῆς εὐθείας, ἀλλʼ εὐθὺς ἀνάγκη ἢ θᾶττον ἢ βραδύτερον, ὥσπερ ἂν εἰ κάταντες, τὸ δʼ ἄναντες·
For it would be absurd if this thing cannot move along a circle in a similar way as that thing moves along a straight line, but we must immediately assume that one is either faster or slower, just as if one were going downhill and the other uphill.
οὐδὲ διαφέρει οὐδὲν τῷ λόγῳ, εἴ τίς φησιν ἀνάγκην εἶναι θᾶττον εὐθὺς ἢ βραδύτερον κινεῖσθαι· ἔσται γὰρ μείζων καὶ ἐλάττων ἡ περιφερὴς τῆς εὐθείας, ὥστε καὶ ἴση.
Nor does it make any difference to the argument if someone says that they must immediately move either faster or slower; for then the circular line will be greater or less than the straight line, and therefore also equal.
εἰ γὰρ ἐν τῷ Α χρόνην τὴν B διλήλυθε τὸ δὲ τὴν Γ. μείζων ἂν εη B τῆς Γ· οὕτω γὰρ τὸ θᾶττον ἐλέγετο.
For if in time A one has traversed the circular line B and the other the straight line C, B would be greater than C; for this is how 'faster' was defined.
οὐκοῦν καὶ εἰ ἐν ἐλάττονι ἴσον, θᾶττον· ὥστʼ ἔσται τι μέρος τοῦ A ἐν τὸ B τοῦ κύκλου τὸ ἴσον δίεισι καὶ τὸ Γ ἐν ὅλῳ τῷ Α.
Therefore, also if it traverses an equal distance in less time, it is faster; so there will be some part of time A in which the object moving on the circle will traverse a part of B equal to C, while the other traverses C in the whole of A.
ἀλλὰ μὴν εἰ ἔστιν συμβλητά, συμβαίνει τὸ ἄρτι ῥηθέν, ἴσην εὐθεῖαν εἶναι κύκλῳ.
But indeed, if they are comparable, the consequence just mentioned follows: that a straight line is equal to a circular line.
ἀλλʼ οὐ συμβλητά οὐδʼ ἄρα αἱ κινήσεις, ἀλλʼ ὅσα μὴ συνώνυμα, πάντʼ ἀσύμβλητα.
But they are not comparable; therefore, neither are their motions. Rather, all things that are not synonymous are incomparable.
οον διὰ τί,οὺ συμβλητὸν πότερον ὀξύτερον τὸ γραφεῖον ἢ ὁ οἶνος ἢ ἡ νήτη;
For example, why is it incomparable whether a pen, wine, or the highest note of a lyre is 'sharper'?
ὅτι ὁμώνυμα, οὐ συμβλητά· ἀλλʼ ἡ νήτη τῇ παρανήτῃ συμβλητή, ὅτι τὸ αὐτὸ σημαίνει τὸ ὀξύ ἐπʼ ἀμφοῖν.
Because they are homonymous, they are incomparable; but the highest note is comparable to the note next to it, because 'sharp' (high) signifies the same thing in both cases.
ἇρʼ οὖν οὐ ταὐτὸν τὸ ταχὺ ἐνταῦθα κἀκεῖ, πολὺ δʼ ἔτι ἦττον ἐν ἀλλοιώσει καὶ φορᾷ;
Is then 'fast' not the same here (in circular motion) and there (in rectilinear motion), and still much less so in alteration and locomotion?
ἢ πρῶτον μὲν τοῦτο οὐκ ἀληθές, ὡς εἰ
μὴ ὁμώνυμα συμβλητά;
Or, first of all, is this not true, that if things are not homonymous they are comparable?
τὸ γὰρ πολὺ τὸ αὐτὸ σημαίνει ἐν ὕδατι καὶ ἀέρι, καὶ οὐ συμβλητά.
For 'much' signifies the same thing in water and in air, yet they are not comparable.
εἰ δὲ μή, τό γε διπλάσιον ταὐτό (δύο γὰρ πρὸς ἕν), καὶ οὐ συμβλητά.
Or if not, at least 'double' is the same (for it is two to one), yet they are not comparable.
ἢ καὶ ἐπὶ τούτων ὁ αὐτὸς λόγος;
Or does the same argument apply also to these?
καὶ γὰρ τὸ πολὺ ὁμώνυμον.
For 'much' is also homonymous.
ἀλλʼ ἐνίων καὶ οἱ λόγοι ὁμώνυμοι, οἷον εἰ λέγοι τις ὅτι τὸ πολὺ τὸ τοσοῦτον καὶ ἔτι, ἄλλο τὸ τοσοῦτον·
But of some things even the definitions are homonymous; for instance, if one were to say that 'much' is 'this much and more', 'this much' is different in different cases.
καὶ τὸ ἴσον ὁμώνυμον, καὶ τὸ ἓν δέ, εἰ ἔτυχεν, εὐθὺς ὁμώνυμον. εἰ δὲ τοῦτο, καὶ τὰ δύο, ἐπεὶ διὰ τί τὰ μὲν συμβλητὰ τὰ δʼ οὔ, εἴπερ ἦν μία φύσις;
And 'equal' is homonymous, and 'one', if it so happens, is immediately homonymous; and if this is so, 'two' is also. For why are some things comparable and others not, if indeed there was a single nature?
ἢ ὅτι ἐν ἄλλῳ πρώτῳ δεκτικῷ;
Or is it because they exist in a different primary receptive subject?
ὁ μὲν οὖν ἵππος καὶ ὁ κύων συμβλητά, πότερον λευκότερον (ἐν γὰρ πρώτῳ, τὸ αὐτό, ἡ ἐπιφάνεια), καὶ κατὰ μέγεθος ὡσαύτως· ὕδωρ δὲ καὶ φωνὴ οὔ· ἐν ἄλλῳ γάρ.
Thus a horse and a dog are comparable as to which is whiter (for the primary subject, the surface, is the same), and similarly in respect of magnitude; but water and voice are not, for they are in different subjects.
ἢ δῆλον ὅτι ἔσται οῦτω γε πάντα ἓν ποιεῖν, ἐν ἄλλῳ δὲ ἕκαστον φάσκειν εἶναι, καὶ ἔσται ταὐτὸ τὸ ἴσον καὶ γλυκὺ καὶ λευκόν, ἀλλʼ ἄλλο ἐν ἄλλῳ;
Or is it clear that in this way one could make everything one, by saying each exists in a different subject, and that 'equal', 'sweet', and 'white' are the same, but different in different subjects?
ἔτι δεκτικὸν οὐ τὸ τυχὸν τοῦ τυχόντος ἐστίν, ἀλλʼ ἓν ἑνὸς τὸ πρῶτον.
Moreover, the receptive subject is not just any random thing for any random property, but one primary subject for one property.