§5.4#2αὗται μὲν οὖν εἰσιν αἱ ἀπορίαι ἔξω τῆς
νῦν σκέψεως· ἐπεὶ δὲ συνεχὴς πᾶσα κίνησις, τήν τε ἁπλῶς μίαν ἀνάγκη καὶ συνεχῆ εἶναι, εἴπερ πᾶσα διαιρετή, καὶ εἰ συνεχής, μίαν.
These difficulties, then, lie outside our present inquiry; but since every motion is continuous, a motion which is absolutely one must also be continuous, if indeed every motion is divisible, and if continuous, one.
οὐ γὰρ πᾶσα γένοιτ’ ἂν συνεχὴς πάσῃ, ὥσπερ οὐδʼ ἄλλο οὐδὲν τῷ τυχόντι τὸ τυχόν, ἀλλʼ ὅσων ἓν τὰ ἔσχατα.
For not any motion could become continuous with any other, just as nothing else can with any chance thing, but only those whose extremes are one.
ἔσχατα δὲ τῶν μὲν οὐκ ἔστι, τῶν δʼ ἔστιν ἄλλα τῷ εἴδει καὶ ὁμώνυμα· πῶς γὰρ ἂν ἅψαιτο ἢ ἓν γένοιτο τὸ ἔσχατον γραμμῆς καὶ βαδίσεως;
But of some things there are no extremes, and of others they are different in species and homonymous; for how could the extreme of a line and that of walking touch or become one?
ἐχόμεναι μὲν οὖν εἶεν ἂν καὶ αἱ μὴ αἱ αὐταὶ τῷ εἴδει μηδὲ τῷ γένει (δραμών γὰρ ἄν τις πυρέξειεν εὐθύς), καὶ οἷον ἡ λαμπὰς ἡ ἐκ διαδοχῆς φορὰ ἐχομένη, συνεχὴς δʼ οὔ.
Hence motions which are not the same in species or even in genus can be consecutive (for a man might immediately get a fever after running), and like the torch-race, a locomotion by succession is consecutive, but not continuous.
κεῖται γὰρ τὸ συνεχές, ὧν τὰ ἔσχατα ἕν.
For the continuous was defined as that of which the extremes are one.
ὥστʼ ἐχόμεναι καὶ ἐφεξῆς εἰσὶ τῷ τὸν χρόνον εἶναι συνεχῆ, συνεχὴς δὲ τῷ τὰς κινήσεις· τοῦτο δʼ, ὅταν ἓν τὸ ἔσχατον γένηται ἀμφοῖν.
So they are consecutive and successive by the time being continuous, but continuous by the motions themselves being continuous; and this occurs when the extreme of both becomes one.
διὸ ἀνάγκη τὴν αὐτὴν εἶναι τῷ εἴδει καὶ ἑνὸς καὶ ἐν ἑνὶ χρόνῳ τὴν ἀπλῶς συνεχῆ κίνησιν καὶ μίαν, τῷ χρόνῳ μέν, ὅπως μὴ ἀκινησία μεταξὺ ᾖ (ἐν τῷ διαλείποντι γὰρ ἠρεμεῖν ἀνάγκη·
Therefore, the motion which is absolutely continuous and one must be the same in species, of one thing, and in one time.
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 μὲν χρόνος εἶς, τῷ εἴδει δʼ ἡ κίνησις ἄλλη·
It must be in one time, so that there may be no immobility in between (for in an interval of time there must be rest; and those motions between which there is rest are many and not one, so that if a motion is interrupted by a standstill, it is neither one nor continuous; and it is interrupted if there is time in between); and in the case of a motion which is not one in species, even if it is not interrupted, the time indeed is one, but the motion is different in species.
τὴν μὲν γὰρ μίαν ἀνάγκη καὶ τῷ εἴδει μίαν εἶναι, ταύτην δʼ ἁπλῶς μίαν οὐκ ἀνάγκη.
For while a single motion must also be one in species, that which is one in species is not necessarily absolutely one.
τίς μὲν οὖν κίνησις ἀπλῶς μία, εἴρηται·
What kind of motion is absolutely one, then, has been said.
ἔτι δὲ λέγεται μία καὶ ἡ τέλειος, ἐάν τε κατὰ γένος ἐάν τε κατʼ εἶδος ἦ ἐάν τε κατʼ οὐσίαν, ὥσπερ καὶ ἐπὶ τῶν ἄλλων τὸ τέλειον καὶ ὅλον τοῦ ἑνός.
Furthermore, a complete motion is also said to be one, whether it be in respect of genus, or of species, or of essence, just as in other things the complete and the whole belong to what is one.
ἔστι δʼ ὅτε κἂν ἀτελὴς ᾖ μία λέγεται, ἐὰν μόνον ᾖ συνεχής.
But sometimes, even if it is incomplete, it is said to be one, provided only that it is continuous.
ἔτι δʼ ἄλλως παρὰ τὰς εἰρημένας λέγεται
μία κίνησις ἡ ὁμαλής.
Moreover, in another way besides those mentioned, a uniform motion is said to be one.
ἡ γὰρ ἀνώμαλος ἔστιν ὡς οὐ δοκεῖ. μία, ἀλλὰ μᾶλλον ἡ ὁμαλής, ὥσπερ ἡ εὐθεῖσ· ἡ γὰρ ἀνώμαλος διαιρετή.
For a non-uniform motion in a way does not seem to be one, but rather the uniform, like a straight line; for the non-uniform is divisible.
ἔοικε δὲ διαφέρειν ὡς τὸ μᾶλλον καὶ ἦττον.
But the difference seems to be one of more and less.
ἔστιν δὲ ἐν ἁπάσῃ κινήσει τὸ ὁμαλῶς ἢ μή· καὶ γὰρ ἂν ἀλλοιοῖτο ὁμαλῶς, καὶ φέροιτο ἐφʼ ὁμαλοῦ οἶον κύκλου ἢ εὐθείας, καὶ περὶ αὔξησιν ὡσαύτως καὶ φθίσιν.
And there is uniformity or its absence in every motion; for a thing might alter uniformly, and be moved along a uniform path, such as a circle or a straight line, and similarly with respect to increase and decrease.
ἀνωμαλία δʼ ἐστὶν διαφορὰ ὁτὲ μὲν ἐφʼ ᾦ 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 οὔτʼ ἐν τῷ πότε οὔτε ἐν τῷ εἰς ὅ, ἀλλʼ ἐν τῷ ὥς. ταχυτῆτι γὰρ καὶ βραδυτῆτι ἐνίοτε διώρισται· ἧς μὲν γὰρ τὸ αὐτὸ τάχος, ὁμαλής, ἧς δὲ μή, ἀνώμαλος.
And non-uniformity is a difference sometimes in that on which the motion occurs (for it is impossible for a motion to be uniform if it is not on a uniform magnitude, for example, motion on a bent line, or on a helix, or on any other magnitude of which any part does not fit on any other part); but sometimes it is neither in the "that which," nor in the "when," nor in the "into what," but in the "how." For it is sometimes defined by quickness and slowness; for that of which the speed is the same is uniform, but that of which it is not, is non-uniform.
διὸ οὐκ εἴδη κινήσεως οὐδὲ διαφοραὶ τάχος καὶ βραδυτής, ὅτι πάσαις ἀκολουθεῖ ταῖς διμαφόροις κατʼ εἶδος.
Therefore, quickness and slowness are not species or differences of motion, because they accompany all motions which are different in species.
ὥστε οὐδὲ βαρύτης καὶ κουφότης ἡ εἰς τὸ αὐτό, οἶον γῆς πρὸς αὐτὴν ἢ πυρὸς πρὸς αὐτό.
Consequently, neither are heaviness and lightness when they are towards the same place, for example, of earth towards itself or of fire towards itself.
μία μὲν οὖν ἡ ἀνώμαλος τῷ συνεχὴς εἶναι, ἧττον δέ, ὅπερ τῇ κεκλασμένῃ συμβαίνει φορᾷ τὸ δʼ ἧττον μίξις αἰεὶ τοῦ ἐναντίου.
A non-uniform motion, then, is one by being continuous, but to a lesser degree, which is what happens in the case of a bent locomotion; and "to a lesser degree" is always a mixture of the contrary.
εἰ δὲ πᾶσαν τὴν μίαν ἐνδέχεται καὶ ὁμαλὴν εἶναι καὶ μή, οὐκ ἂν εἴησαν αἱ ἐχόμεναι αἱ μὴ κατʼ εἶδος αἱ αὐται μία καὶ συνεχής·
But if every single motion can be both uniform and non-uniform, then motions which are consecutive but not the same in species cannot be one and continuous.
πῶς γὰρ ἂν εἴη ὁμαλὴς ἠ ἐξ ἀλλοιώσεως συγκειμένη καὶ φορᾶς;
For how could a motion composed of alteration and locomotion be uniform?
δέοι γὰρ ἂν ἐφαρμόττειν.
For they would have to fit on one another.