§3.1Διὰ τί κινοῦσι μεγάλα βάρη μικραὶ δυνάμμεις τῷ μοχλῷ. ὥσπερ ἐλέχθη καὶ κατ’ἀρχήν, προσλαβόντι βάρος ἔτι τὸ τοῦ μοχλοῦ;
Why is it that small forces move great weights by means of a lever, even, as was also said at the beginning, when the weight of the lever itself is further added?
Ῥᾷον δὲ τὸ ἔλαττόν ἐστι κινῆσαι βάρος, ἔλαττον δέ ἐστιν ἄνευ τοῦ μοχλοῦ, Ἥ ὅτι αἴτιόν ἐστιν ὁ μοχλός, ζυγὸν [ὢν] κάτωθεν ἔχον τὸ σπαρτίον καὶ εἰς ἄνισα διῃρημένον;
It is easier to move a smaller weight, and the weight is less without the lever. Or is it because the lever is the cause, being a balance which has its cord below and is divided into unequal parts?
Τὸ γὰρ ὑπομόχλιον ἀντὶ σπαρτίου γίνεται· μένει γὰρ ἄμφω ταῦτα, ὥσπερ τὸ κέντρον.
For the fulcrum becomes instead of a cord; for both of these remain stationary, like the center.
§3.2Ἐπεὶ δὲ θᾶττον ὑπὸ τοῦ ἴσου βάρους κινεῖται ἡ μείζων τῶν ἐκ τοῦ κέντρου, ἔστι δὲ τρία τὰ περὶ τὸν μοχλόν, τὸ μὲν ὑπομόχλιον, σπάρτον καὶ κέντρον, δύο δὲ βάρη, ὅ τε κινῶν καὶ τὸ κινούμενον· ὃ οὖν τὸ κινούμενον βάρος πρὸς τὸ κινοῦν, τὸ μῆκος πρὸς τὸ μῆκος ἀντιπέπονθεν.
And since the greater of the radii from the center is moved more quickly by an equal weight, and there are three things concerning the lever—the fulcrum, which is the cord and center, and two weights, the mover and the moved— therefore, the ratio of the moved weight to the moving weight is inversely proportional to the ratio of the length to the length.
Αἰεὶ δὲ ὅσῳ ἂν μεῖζονἀφεστήκῃ τοῦ ὑπομοχλίου, ῥᾷον κινήσει.
And always, by how much further it is distant from the fulcrum, by so much more easily will it move.
§3.3Αἰτία δέ ἐστιν ἡ προλεχθεῖσα, ὅτι ἡ πλεῖον ἀπέχουσα ἐκ τοῦ κέντρου μείζονα κύκλον γράφει.
The cause is that which was said before, namely that the line which is further from the center describes a larger circle.
Ὤστε ἀπὸ τῆς αὐτῆς ἰσχύος πλέονμετανοῦσιν· στήσεται τὸ κινοῦν τὸ πλεῖον τοῦ ὑπομοχλίου ἀπέχον.
Therefore, they move more from the same force; the moving force which is further from the fulcrum will stand.
Ἔστω μοχλὸς ἐφ’ οὗ ΑΒ. βάρος δὲ ἐφ’ ᾧ τὸ Γ, τὸ δὲ κινοῦν ἐφ’ ᾧ τὸ Δ, ὑπομόχλιον ἐφ’ ᾧ τὸ Ε, τὸ δὲ ἐφ’ ᾧ τὸ Δ κινῆσαν ἐφ’ ᾧ τὸ Η, κινούμενον δὲτὸ ἐφ’ οὖ Γ, βάρος ἐφ’ οὖ Κ.
Let there be a lever AB, and the weight G, and the mover D, and the fulcrum E, and let the mover D have moved to H, and the moved weight at G be K.