§5.1Διὰ τί τὸ πηδάλιον μικρὸν ὅν, καὶ ἐπ’ ἐσχάτῳ τῷ πλοίῳ, τοσαύτην δύναμιν ἔχει ὥστε ὑπὸ μικροῦ οἴακος καὶ ἑνὸς ἀνθρώπου δυνάμεως, καὶ ταύτης ἠρεμαίας,μεγάλακινεῖσθαιμεγέθη πλοίων;
Why is it that the rudder, being small and at the very end of the vessel, has such great power that, by a small tiller and the power of one man, and that a gentle one, great bulks of ships are moved?
Ἢ διότι καὶ τὸ πηδάλιόν ἐστι μοχλός, καὶ μοχλεύει ὁ κυβερνήτης.
Or is it because the rudder is also a lever, and the helmsman uses it as a lever?
Ἦι μὲν οὖν προσήρμοσται τῷ πλοίῳ, γίνεται ὑπομόχλιον, τὸ δὲ ὅλον πηδάλιον ὁ μοχλός, τὸ δὲ βάρος ἡ θάλασσα, ὁ δὲ κυβερνήτης ὁ κινῶν.
The part where it is attached to the ship becomes the fulcrum, the whole rudder is the lever, the weight is the sea, and the helmsman is the mover.
§5.2Οὐ κατὰ πλάτος δὲ λαμβάνει τὴν θάλασσαν, ὥσπερ ἡ κώπη, τὸ πηδάλιον. Οὐ γὰρ εἰς τὸ πρόσθεν κινεῖ τὸπλοῖον, ἀλλὰ κινούμενον κλίνει, πλαγίως τὴν θάλατταν δεχόμενον.
But the rudder does not take the sea broadside like the oar; for it does not move the ship forward, but as it is moved, it inclines it, receiving the sea obliquely.
Ἐπεὶ γὰρ τὸ βάρος ἧω ἡ θάλασσα, τοὐναντίον ἀπερειδόμενον κλίνει τὸ πλοῖον.
For since the sea was the weight, by pressing against it, it inclines the ship in the opposite direction.
Τὸ γὰρ ὑπομόχλιον εἰς τοὐναντίον στρέφεται, ἡ θάλασσα δὲ ἐντός· ἐκεῖνο δὲ εἰς τὸ ἐκτός.
For the fulcrum turns in the opposite direction, while the sea is on the inside and the former [the fulcrum] is on the outside.
§5.3Τούτῳ δὲ ἀκολουθεῖ τὸπλοῖον διὰ τὸ συνδεδέσθαι.
And the ship follows this because of being bound to it.
Ἡ μὲν οὖν κώπη κατὰ πλάτος τὸ βάρος ὠθοῦσα καὶ ὑπ’ ἐκείνουἀντωθουμένη εἰς τὸ εὐθύ προάγει· τὸ δὲ πηδάλιον, ὥσπερ κάθηται πλάγιον, τὴν εἰς τὸ πλάγιον, ἢ δεῦρο ἢ ἐκεῖ, ποιεῖ κίνησιν.
Now the oar, pushing the weight broadside and being pushed back by it, propels straight forward; but the rudder, just as it is situated obliquely, produces a motion to the side, either here or there.
§5.4Ἐπ’ ἄκρου δὲ καὶ οὐκ ἐν μέσῳ κεῖται, ὅτι ῥᾷστον τὸ κινούμενον κινῆσαι ἀπ’ ἄκρου κινοῦν. Τάχιστα γὰρ φέρεται τὸ πρῶτον μέρος διὰ τὸ ὥσπερ ἐν τοῖς φερομένοις ἐπὶ τέλει λήγειν τὴν φοράν, οὕτω καὶ τοῦ συνεχοῦς ἐπὶ τέλους ἀσθενεστάτη ἐστὶν ἡ φορά.
And it is placed at the end and not in the middle because it is easiest to move a moving thing by moving it from the end; for the first part is carried fastest because, just as in things that are carried, the motion ceases at the end, so also at the end of a continuous body the motion is weakest.
§5.5Εἰ δὲ ἀσθενεστάτη, ῥᾳδία ἐκκρούειν.
And if it is weakest, it is easy to push aside.
Διά τε δὴ ταῦτα ἐν τῇ πρύμνῃ τὸ πηδάλιόν ἐστι, καὶ ὅτι ἐνταῦθα μικρᾶς κινήσεως γενομένης πολλῷ μεῖζον τὸ διάστημα ἐπὶ τῷ ἐσχάτῳ γίνεται, διὰ τὸ τὴν ἴσην γωνίαν ἐπὶ μείζονα καθῆσθαι, καὶ ὅσῳ ἂν μείζους ὦσιν αἱ περιέχουσαι.
It is both for these reasons, then, that the rudder is at the stern, and because there, a small movement being made, the distance at the extreme end becomes much greater, because the same angle subtends a greater distance, by how much the containing lines are greater.
§5.6Δῆλον δὲ ἐκ τούτου καὶ δι’ ἣν αἰτίαν μᾶλλον προέρχεται εἰς τοὐναντίον τὸ πλοῖον ἢ ἡ τῆς κώπης πλάτη· τὸ αὐτὸ γὰρ μέγεθος τῇ αὐτῇ ἰσχύϊ κινούμενον ἐν ἀέρι πλέον ἢ ἐν τῷ ὕδατι πρόεισιν.
And from this it is also clear for what reason the ship proceeds further in the opposite direction than the blade of the oar does; for the same size moved by the same force proceeds further in air than in water.
Ἕστω γὰρ ἡ Α Β κώπη, τὸ δὲ Γ ὁ σκαλμός, τὸ δὲ Α τὸ ἐν. τῷ πλοίῳ, ἡ ἀρχὴ τῆς κώπης, τὸ δὲ Β τὸ ἐν τῇθαλάττῃ.
For let AB be the oar, Γ the tholepin, A the end of the oar inside the ship (the beginning of the oar), and B the part in the sea.
§5.7Εἰ δἡ τὸ Α οὗ τὸ Δ μετακεκίνηται, τὸ Β οὐκ ἔσται οὗ τὸ Ε· ἴση γὰρ ἡ Β Ετῇ ΑΔ. Ἵσον οὖν μετακεχωρηκὸς ἔσται.
If indeed A has moved to where Δ is, B will not be where E is; for BE is equal to AD, so it would have moved an equal distance.
Ἀλλ’ ἦν ἔλαττον.
But it was less.
Ἕσται δὴ οὗ τὸΖ ἢ τὸ Θ. Ἅρα τοίνυν τὴν Α Β, καὶ οὐχ ἡ τὸ Γ, καὶ κάτωθεν.
It will, therefore, be where Ζ or Θ is. Therefore, AB moves as a whole and not at Γ, and from below.
Ἐλάττων γὰρ ἡ ΒΖ τῆς Α Δ, ὥστε καὶ ἡ ΘΖ τῆς ΔΘ· ὅμοια γὰρ τὰ τρίγωνα.
For BZ is less than AD, so that ΘZ is also less than ΔΘ; for the triangles are similar.
§5.8Καθεστηκὸς δὲ ἔσται καὶ τὸ μέσον, τὸ ἐφ’ οὗ Γ· εἰς τοὐναντίον γὰρ τῷ ἐν τῇ θαλάττῃ ἄκρῳ τῷ Β μεταχωρεῖ, ᾗπερ τὸ ἐν τῷ πλοίῳ ἄκρον τὸ Α μὴ ἐχώρει οὖ τὸ Δ. Ὤστε μετακινηθήσεται τὸ πλοῖον, καὶ ἐκεῖ οὗ ἡ ἀρχὴ τῆς κώπης μεταφέρεται.
And the middle part, on which Γ is, will also be shifted; for it shifts in the opposite direction to the end B in the sea, where the end A in the ship did not shift to where Δ is. Consequently, the ship will be moved, and in that direction where the beginning of the oar is carried.
§5.9Τὸ δ’ αὐτὸ καὶ τὸ πηδάλιον ποιεῖ, πλὴν ὅτι εἰς τὸ πρόσθεν οὐδὲν συμβάλλεται τῷ πλοίῳ, ὥσπερ ἐλέχθη ἐπὶ ἄνω, ἀλλὰ μόνον τὴν πρύμναν εἰς τὸ πλάγιον ἀπωθεῖ ἔνθα ἢ ἔνθα· εἰς τοὐναντίον γὰρ ἡ πρῷρα οὕτω νεύει.
And the rudder does the very same thing, except that it contributes nothing to the forward progress of the ship, as was said above, but only pushes the stern sideways here or there; for the prow inclines in the opposite direction in this way.
§5.10Ἦι μὲν δὴ τὸ πηδάλιον προσέζευκται, δεῖ οἶόν τι τοῦ κινουμένου μέσον νοεῖν, καὶ ὥσπερ ὁ σκαλμὸς τῇ κώπῃ· τὸ δὲ μέσον ὑποχωρεῖ, ᾖ ὁ οἴαξ μετακινεῖται.
The part where the rudder is joined must be conceived as a sort of center of the moving thing, just as the tholepin is to the oar; and the middle retreats in the direction where the tiller is moved.
Ἐὰν μὲν εἴσω ἄγῃ, καὶ ἡ πρύμνα δεῦρο μεθέστηκεν· ἡ δὲ πρῷρα εἰς τοὐναντίον νεύει· ἐν γὰρ τῷ αὐτῷ οὔσης τῆς πρῷρας τὸ πλοῖον μεθέστηκεν ὅλον.
If indeed one leads it inward, the stern also shifts here; and the prow inclines in the opposite direction; for while the prow is in the same place, the whole ship shifts.