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Aristotle · Mechanics §14.1

Why Wood Breaks More Easily When Held Far from the Fulcrum

Passage 16 of 38 · Greek

Summary

Explains why a piece of wood is broken more easily when held further from the fulcrum (the knee or the foot) by relating it to the principle that objects further from the center of circular motion are moved more easily.

§14.1Διὰ τί τὸ αὐτὸ μέγεθος ξύλον ῥᾷον κατεάσσεται περὶ τὸ γόνυ, ἐὰν ἴσὸνἀποστήσας τῶν ἄκρων ἐχόμενος καταγνύῃ, ἢπαρὰ τὸ γόνυ ἐγγὺς ὄντος·
Why is a piece of wood of the same size broken more easily around the knee, if one breaks it holding it at an equal distance from the ends, than if the grip is near the knee?
καὶ ἐὰν πρὸς τὴν γῆν ἐρείσας καὶ τῷ ποδὶ προσβὰς πόρρωθεν τῇ χειρὶ καταγνύῃ, ἢ ἐγγύθεν;
And if, leaning it against the ground and stepping on it with the foot, one breaks it with the hand from a distance, rather than from near by?
Ἥ διότι ἔνθαμὲν τὸ γόνυ κέντρον, ἔνθα δὲ ὁ πούς.
Or is it because in the former case the knee is the center, and in the latter the foot?
Ὄσῳ δ’ ἂν πορρώτερον ᾖ τοῦ κέντρου, ῥᾷον κινεῖται ἅπαν. Κινηθῆναι δὲ ἀνάγκη καταγνύμενον.
For the further it is from the center, the more easily everything is moved; and that which is broken must of necessity be moved.

Notes

  1. §14.1ἴσον ἀποστήσας τῶν ἄκρων — ἀποστήσας is an aorist active participle in the nominative singular, agreeing with the implied subject of καταγνύῃ (the general 'one'). τῶν ἄκρων is a genitive of separation meaning 'from the ends,' which, combined with the adverbial accusative ἴσον ('equally'), means 'keeping an equal distance from the ends (i.e., at both ends)'.
  2. §14.1ἐγγὺς ὄντος — A genitive absolute construction where the genitive subject (such as τοῦ ἐχομένου 'the part held' or τοῦ κρατοῦντος 'the hand holding') is omitted, meaning 'when the grip is near the knee,' in contrast to holding it further away.
  3. §14.1Κινηθῆναι δὲ ἀνάγκη καταγνύμενον — An impersonal construction with ἀνάγκη ('it is necessary'). καταγνύμενον is a present passive participle in the neuter singular (nominative or accusative), functioning substantively as 'that which is being broken,' and serves as the subject of the passive infinitive κινηθῆναι ('to be moved').

Cite this passage

Aristotle, Mechanics §14.1. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg023.humanitext-grc1:14.1

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