§22.1Διὰ τί τὰ κάρυα ῥᾳδίως καταγνύουσιν ἄνευ πληγῆς ἐν τοῖς ὀργάνοις ἂ ποιοῦσι πρὸς τὸ καταγνύναι αὐτά;
Why is it that people easily crack nuts without a blow, in the instruments which they make for cracking them?
Πολλὴ γὰρ ἀφαιρεῖται ἰσχὺς ἡ τῆς φορᾶς καὶ βίας, Ἔτι δὲ σκληρῷ καὶ βαρεῖ συνθλίβων θᾶττον ἄν κατάξαι ἢ ξυλίνῳ καὶ κούφῳ τῷ ὀργάνῳ.
For much force, namely that of motion and violence, is taken away [without a blow]. Moreover, one would crack [them] more quickly by crushing with a hard and heavy object than with a wooden and light instrument.
§22.2Ἣ διότι οὕτως ἐπ’ ἀμφότερα θλίβεται ὑπὸ δύο μοχλῶν τὸ κάρυον, τῷ δὲ μοχλῷ ῥᾳδίως διαιρεῖται τὰ βάρη;
Or is it because the nut is thus squeezed on both sides by two levers, and by the lever weights (resistances) are easily divided?
Τὸ γὰρ ὄργανον ἐκ δύο σύγκειται μοχλῶν, ὑπομόχλιον ἐχόντων τὸ αὐτό, τὴν συναφὴν ἐφ’ᾖς τὸ Α.
For the instrument consists of two levers, having the same fulcrum, namely the joint at A.
§22.3Ὥσπερ οὖν εἰ ἦσαν ἐκβεβλημέναι, ὑφ’ ὦν κινουμένων εἰς τὰ τῶν ΓΔ ἄκρα αἱ ΕΖ συνήγοντο ῥᾳδίως ἀπὸ μικρᾶς ἰσχύος· ἢν οὖν ἐν τῇ πληγῇ τὸ βάρος ἐποίει, ταύτην ἡ κρείττων ταύτης, ἡ τὸ ΕΓ καὶ ΖΔ, μοχλοὶ ὄντες ποιοῦσι· τῇ ἄρσει γὰρ εἰς τοὐναντίοναἴρονται, καὶ θλίβοντες καταγνύουσι τὸ ἐφ’ ᾦ Κ.
Therefore, just as if they had been produced (extended), by the movement of which towards the extremities of Γ and Δ, the points Ε and Ζ are easily brought together by a small force; therefore, the force which the blow would have produced, this the levers ΕΓ and ΖΔ, being levers, produce as a force greater than that; for by the counter-pressure they are raised in the opposite direction, and by squeezing they crack that which is at Κ.
§22.4Δι’ αὐτὸ δὲ τοῦτο καὶ ὅσῳ ἂν ἐγγύτερον ᾖ τῆς Α τὸ Κ, συντρίβεται θᾶττον· ὅσῳ γὰρ ἄν πλέον ἀπέχῃ τοῦ ὑπομοχλίον ὁ μοχλός, ῥᾷον κινεῖ καὶ πλεῖον ἀπὸ τῆς ἰσχύος τῆς αὐτῆς.
For this very reason, the closer Κ is to A, the more quickly it is crushed; for the further the lever [where the power is applied] is from the fulcrum, the more easily and the more it moves [the weight] by the same force.
Ἔστιν οὖν τὸ μὲν Α ὑπομόχλιον, ἡ δὲ ΔΑΖ μοχλός, καὶ ἡ ΓΑΕ.
Therefore, A is the fulcrum, and ΔΑΖ is a lever, and ΓΑΕ is [a lever].
§22.5Ὄσῳ ἂν οὖν τὸ Κ ἐγγντέρω ᾖ τῆς γωνίας τῶν Α, τοσούτῳ ἐγγύτερον γίνεται τῆς συναφῆς τῶν Α· τοῦτο δέ ἐστι τὸ ὑπομόχλιον.
Therefore, the closer Κ is to the angle of A, the closer it becomes to the joint of A; and this is the fulcrum.
Ἀνάγκη τοίνυν ἀπὸ τῆς αὐτῆς ἰσχύος συναγούσης τὸ Ζ Ε αἴρεσθαι πλέον.
It is necessary, then, that by the same force which brings Ζ and Ε together, more movement is produced.
Ὤστε ἐπεί ἐστιν ἐξ ἐναντίας ἡ ἄρσις, ἀνάγκη θλίβεσθαι μᾶλλον· τὸ δὲ μᾶλλον θλιβόμενον κατάγνυται θᾶττον.
Consequently, since the pressure is from opposite sides, it must be squeezed more; and that which is squeezed more is cracked more quickly.