§9Ὅτι μὲν οὖν ἀρτίους ἔχει τοὺς πόδας πάντα, καὶ διὰ 9 τίνʼ αἰτίαν εἴρηται·
Therefore, it has been stated that all animals have an even number of feet, and for 9 what cause.
ὅτι δʼ εἰ μηθὲν ἦν ἠρεμοῦν, οὐκ ἂν ἦν κάμψις οὐδʼ εὔθυνσις, ἐκ τῶνδε δῆλον.
But that if there were nothing at rest, there would be no bending or straightening, is clear from what follows.
ἔστι γὰρ κάμψις μὲν ἡ ἐξ εὐθέος ἢ εἰς περιφερὲς ἢ εἰς γωνίαν μεταβολή, εὔθυνσις δʼ ἡ ἐκ θατέρου τούτων εἰς εὐθύ.
For bending is a change from a straight line to either a curved line or an angle, and straightening is a change from either of these to a straight line.
ἐν ἁπάσαις δὲ ταῖς εἰρημέναις μεταβολαῖς ἀνάγκη πρὸς ἓν σημεῖον τὴν κάμψιν ἢ τὴν εὔθυνσιν γίνεσθαι.
And in all the mentioned changes, it is necessary for the bending or straightening to occur in relation to one point.
ἀλλὰ μὴν κάμψεώς γε μὴ οὔσης οὔτʼ ἂν πορεία οὔτε νεῦσις οὔτε πτῆσις ἦν.
However, if there were no bending, there would be neither walking, swimming, nor flying.
τὰ μὲν γὰρ ὑπόποδα ἐπειδὴ ἐν ἑκατέρῳ τῶν ἀντικειμένων σκελῶν ἐν μέρει ἵσταται καὶ τὸ βάρος ἴσχει, ἀναγκαῖον θατέρου προβαίνοντος θατέρου ποιεῖσθαι κάμψιν.
For since footed animals stand alternately on each of their opposite legs and support their weight, it is necessary, as one advances, for the other to perform a bending.
ἴσα τε γὰρ πέφυκεν ἔχειν τῷ μήκει τὰ ἀντίστοιχα κῶλα, καὶ ὀρθὸν δεῖ εἶναι τὸ ὑφεστὸς τῷ βάρει, οἷον κάθετον πρὸς τὴν γῆν.
For the corresponding limbs are by nature equal in length, and the one supporting the weight must be upright, as it were perpendicular to the ground.
ὅταν δὲ προβαίνῃ, γίνεται ἡ ὑποτείνουσα καὶ δυναμένη τὸ μένον μέγεθος καὶ τὴν μεταξύ.
But when it advances, there is formed the hypotenuse, which is equal in power to the remaining magnitude and the distance between them.
ἐπεὶ δʼ ἴσα τὰ κῶλα, ἀνάγκη κάμψαι τὸ μένον, ἢ ἐν τῷ γόνατι ἢ ἐν τῇ κάμψει, οἷον εἴ τι ἀγόνατον εἴη τῶν βαδιζόντων.
Since the limbs are equal, it is necessary to bend the remaining one, either at the knee or at the joint, if any of the walking animals should be without knees.
σημεῖον δʼ ὅτι οὕτως ἔχει· εἰ γάρ τις ἐν γῇ βαδίζοι παρὰ τοῖχον, ἡ γραφομένη ἔσται οὐκ εὐθεῖα ἀλλὰ σκολιά, διὰ τὸ ἐλάττω μὲν κάμπτοντος γίνεσθαι τὴν γραφομένην, μείζω δʼ ἱσταμένου καὶ ἐξαίροντος.
A proof that this is so is the following: if someone walks on the ground along a wall, the line drawn will be not straight but winding, because the drawn line becomes lower when he bends, and higher when he stands upright and raises himself.
ἐνδέχεται μέντοι κινεῖσθαι καὶ μὴ ἔχοντος καμπὴν τοῦ σκέλους, ὥσπερ τὰ παιδία ἕρπουσι.
However, it is possible to move even if the leg does not have a bend, just as infants crawl.
καὶ περὶ τῶν ἐλεφάντων ὁ παλαιὸς ἦν λόγος τοιοῦτος, οὐκ ἀληθὴς ὤν.
And concerning elephants, the ancient story was of this kind, though it is not true.
κινεῖται δὲ καὶ τὰ τοιαῦτα κάμψεως γινομένης ἐν ταῖς ὠμοπλάταις ἢ τοῖς ἰσχίοις.
But even such things move by a bending occurring in their shoulder blades or hips.
ἀλλʼ ὀρθὸν οὐδὲν δύναιτʼ ἂν πορευθῆναι συνεχῶς καὶ ἀσφαλῶς, κινηθείη δʼ ἂν οἷον ἐν ταῖς παλαίστραις οἱ διὰ τῆς κόνεως προϊόντες ἐπὶ τῶν γονάτων·
Yet nothing could walk upright continuously and safely; rather, it would move like those who advance on their knees through the dust in wrestling schools.
πολὺ γὰρ τὸ ἄνω μέρος, ὥστε δεῖ μακρὸν εἶναι τὸ κῶλον· εἰ δὲ τοῦτο, κάμψιν ἀναγκαῖον εἶναι.
For the upper part is large, so that the limb must be long; and if this is so, there must of necessity be bending.
ἐπεὶ γὰρ ἕστηκε πρὸς ὀρθήν, εἰ ἄκαμπτον ἔσται τὸ κινούμενον εἰς τὸ πρόσθεν, ἢ καταπεσεῖται ἐλάττονος τῆς ὀρθῆς γινομένης, ἢ οὐ προβήσεται.
For since it stands at a right angle, if the part moving forward is to be unbent, it will either fall down as the angle becomes less than a right angle, or it will not advance.
εἰ γὰρ ὀρθοῦ ὄντος θατέρου σκέλους θάτερον ἔσταιπροβεβηκός, μεῖζον ἔσται, ἴσον ὄν· δυνήσεται γὰρ τοῦτο τό τʼ ἠρεμοῦν καὶ τὴν ὑποτείνουσαν.
For if, while one leg is upright, the other has advanced, it will be greater, though they are equal; for this [advancing leg] will be equal in power to both the resting leg and the hypotenuse.
ἀνάγκη ἄρα κάμπτεσθαι τό τε προϊόν, καὶ κάμψαν ἅμα ἐκτείνειν θάτερον, ἐκκλίνειν τε καὶ διαβεβηκέναι καὶ ἐπὶ τῆς καθέτου μένειν· ἰσοσκελὲς γὰρ γίνεται τρίγωνον τὰ κῶλα, καὶ ἡ κεφαλὴ γίνεται κατώτερον, ὅταν κάθετος ἐφʼ ἧς βέβηκε.
It is necessary, then, for the advancing leg to bend, and while bending, at the same time to extend the other, to lean forward, to stride, and to remain on the perpendicular; for the limbs form an isosceles triangle, and the head becomes lower when the perpendicular is that on which it stands.
τὰ δʼ ἄποδα τὰ μὲν κυμαίνοντα προέρχεται (τοῦτο δὲ διττῶς συμβαίνει· τὰ μὲν γὰρ ἐπὶ τῆς γῆς, καθάπερ οἱ ὄφεις, τὰς καμπὰς ποιεῖται, τὰ δʼ εἰς τὸ ἄνω, ὥσπερ αἱ κάμπαι), ἡ δὲ κύμανσις καμπή ἐστι· τὰ δʼ ἰλυσπάσει χρώμενα, καθάπερ τὰ καλούμενα γῆς ἔντερα καὶ βδέλλαι.
On the other hand, footless animals, some advance by undulating (and this happens in two ways: for some undulate on the ground, like snakes, and others upward, like caterpillars), and undulation is a bending; others use crawling, like the so-called earthworms and leeches.
ταῦτα γὰρ τῷ μὲν ἡγουμένῳ προέρχεται, τὸ δὲ λοιπὸν σῶμα πᾶν πρὸς τοῦτο συνάγουσι, καὶ τοῦτον τὸν τρόπον εἰς τόπον ἐκ τόπου μεταβάλλουσι.
For these advance with their leading part, and then draw the rest of their body toward this, and in this manner they change from place to place.
φανερὸν δʼ ὅτι εἰ μὴ αἱ δύο τῆς μιᾶς μείζους ἦσαν, οὐκ ἂν ἐδύναντο κινεῖσθαι τὰ κυμαίνοντα τῶν ζῴων.
And it is clear that if the two sides were not greater than the one, the undulating animals would not be able to move.
ἐκταθείσης γὰρ τῆς καμπῆς, εἰ ἴσην κατεῖχεν, οὐθὲν ἂν προῄεσαν· νῦν δʼ ὑπερβάλλει ἐκταθεῖσα, καὶ ἠρεμήσαντος τούτου ἐπάγει τὸ λοιπόν.
For when the bend is extended, if it occupied an equal length, they would not advance at all; but as it is, when extended, it exceeds [the original length], and when this part has come to rest, it brings up the rest.
ἐν ἀπάσαις δὲ ταῖς λεχθείσαις μεταβολαῖς τὸ κινούμενον ὁτὲ μὲν ἐκτεινόμενον εἰς εὐθὺ προέρχεται, ὁτὲ δὲ συγκαμπτόμενον, τοῖς μὲν ἡγουμένοις μέρεσιν εὐθὺ γινόμενον, τοῖς δʼ ἑπομένοις συγκαμπτόν.
And in all the mentioned changes, the moving object at one time advances by extending into a straight line, and at another by bending together, becoming straight in its leading parts and bending together in its following parts.
ποιεῖται δὲ καὶ τὰ ἁλλόμενα πάντα τὴν κάμψιν ἐν τῷ ὑποκειμένῳ μέρει τοῦ σώματος, καὶ τοῦτον τὸν τρόπον ἔχοντα ἅλλεται.
All jumping animals also make their bend in the underlying part of their body, and having themselves in this manner, they jump.
καὶ τὰ πετόμενα δὲ καὶ τὰ νέοντα, τὰ μὲν τὰς πτέρυγας εὐθύνοντα καὶ κάμπτοντα πέταται, τὰ δὲ τοῖς πτερυγίοις, καὶ τούτων τὰ μὲν τέτταρσι τὰ δὲ δυσίν, ὅσα προμηκέστερα τὴν μορφήν, ὥσπερ τὸ τῶν ἐγχελύων γένος· τὴν δὲ λοιπὴν κίνησιν ἀντὶ τῶν δύο πτερυγίων τῷ λοιπῷ τοῦ σώματος καμπτόμενα νεῖ, καθάπερ εἴρηται πρότερον.
And flying and swimming animals likewise; some fly by straightening and bending their wings, others with their fins—and of these, some with four, others with two, those that are more elongated in form, like the family of eels; and they perform the rest of their movement by bending the rest of their body instead of the two fins, as has been said before.
οἱ δὲ πλατεῖς τῶν ἰχθύων τῇ μὲν τῷ πλάτει χρῶνται τοῦ σώματος ἀντὶ πτερυγίων, τῇ δὲ πτερυγίοις δυσί.
Flat fish use the flat part of their body instead of fins, and others use two fins.
τὰ δὲ πάμπαν πλατέα, καθάπερ ὁ βάτος, αὐτοῖς τοῖς πτερυγίοις καὶ ταῖς ἐσχάταις τοῦ σώματος περιφερείαις εὐθύνοντα καὶ κάμπτοντα ποιεῖται τὴν νεῦσιν.
Those that are entirely flat, like the skate, make their swimming by straightening and bending their fins themselves and the outermost edges of their body.