§16.1Διὰ τί,ὅσῳ ἂν ᾖ μακρότερα τὰ ξύλα, τοσούτῳ ἀσθενέστερα γίνεται, καὶ κάμπτεται αἰρομένα μᾶλλον,κἂν ᾖ τὸ μὲν βραχύ, ὅσον δίπηχυ, λεπτόν, τὸ δὲ ἑκατὸν πηχῶν παχύ;
Why is it that the longer pieces of wood are, the weaker they become, and the more they bend when raised, even if the short piece is thin, say two cubits long, and the other is thick, a hundred cubits long?
Ἢ διότι μοχλὸς γίνεται καὶ βάρος καὶ ὑπομόχλιον ἐν τῷ αἴρεσθαι τοῦ ξύλου τὸ μῆκος;
Or is it because, when it is raised, the length of the wood becomes a lever, a weight, and a fulcrum?
Τὸ μὲν γὰρ πρῶτον μέρος αὐτοῦ,ὃ ἡ χεὶρ αἴρει, οἷον ὑπομόχλιον γίνεται,τὸ δ’ ἐπὶ τῷ ἄκρῳ βάρος.
For its first part, which the hand raises, becomes as it were a fulcrum, and the part at the extremity becomes the weight.
§16.2Ὥστε ὅσῳ ἄν ᾖ μακρότερον τὸ ἀπὸ τοῦ ὑπομοχλίου, τοσούτῳ ἀνάγκη κάμπτεσθαιμᾶλλον· ὅσῳ γὰρ ἂν πλέον ἀπέχῃ τοῦ ὑπομοχλίου, τοσούτῳ ἀνάγκη κάμπτεσθαι μεῖζον.
Consequently, the longer the part extending from the fulcrum is, the more it must of necessity bend; for the further it is distant from the fulcrum, the more greatly it must of necessity bend.
Ἀνάγκη οὖν αἴρεσθαι τὰ ἄκρα τοῦ μοχλοῦ.
It is necessary, then, for the extremities of the lever to be raised.
Ἐὰν οὖν ᾖ καμπτόμενος ὁ μοχλός, ἀνάγκη αὐτὸν κάμπτεσθαι μᾶλλον αἰρόμενον.
If, therefore, the lever is bendable, it must of necessity bend more when raised.
Ὅπερ συμβαίνει ἐπὶ τῶν ξύλων τῶν μακρῶν· ἐν δὲ τοῖς βραχέσιν ἐγγύς τὸ ἔσχατον τοῦ ὑπομοχλίου γίνεται τοῦ ἠρεμοῦντος.
This is indeed what happens in the case of long pieces of wood; whereas in short ones, the extremity is close to the fulcrum which remains at rest.