Aristotle · Mechanics §17.1-17.2

Why a Small Wedge Can Split Large Bodies

Passage 19 of 38 · Greek

Summary

This section explains how a small wedge splits large objects by treating it as two opposing levers and analyzing the impact of the blow's momentum and velocity.

§17.1Διὰ τί τῷ σφηνὶ ὄντι μικρῷ μεγάλα βάρη διίσταται καὶ μεγέθη σωμάτων, καὶ θλῖψις ἰσχυρὰ γίνεται;

Why is it that, although the wedge is small, great weights and large bodies are split apart by it, and strong pressure is produced?

Ἢ διότι ὁ σφὴν δύο μοχλοί εἰσιν ἐναντίοι ἀλλήλοις, ἔχει δὲ ἑκάτερος τὸ μὲν βάρος τὸ δὲ ὑπομόχλιον, ὃ καὶ ἀνασπᾷ ἢ πιέζει.

Or is it because the wedge consists of two levers opposed to each other, and each has a weight and a fulcrum, which indeed pries up or presses down?

Ἕτι δὲ ἡ τῆς πληγῆς φορὰ τὸ βάρος, ὃ τύπτει καὶ κινεῖ,ποιεῖ μέγα· καὶ διὰ τὸ κινούμενον κινεῖν τῇ ταχυτῆτι ἰσχύει ἔτι πλέον.

Furthermore, the momentum of the blow makes the weight, which strikes and moves, great; and because that which is in motion moves by its velocity, it is still more powerful.

§17.2Μικρῷ δὲ ὄντι μεγάλαι δυνάμεις ἀκολουθοῦσι· διὸ λανθάνει κινῶνπαρὰ τὴν ἀξίαν τοῦ μεγέθους.

Though it is small, great forces attend it; wherefore it escapes notice that it moves things beyond what is proportional to its size.

Ἔστω σφὴν ἐφ’ ᾧ ΑΒΓ, τὸ δὲ σφηνούμενονΔΕΗΖ. Μοχλὸς δὴ γίνεται ἡ ΑΒ, βάρος δὲ τὸτοῦ Β κάτωθεν, ὑπομόχλιον δὲ τὸ ΖΔ. Ἐναντίος δὲ τούτῳ μοχλὸς τὸ ΒΓ, Ἡ δὲ ΑΓ κοπτομένη ἑκατέρᾳ τούτων χρῆται μοχλῷ· ἀνασπᾷ γὰρ τὸ Β.

Let there be a wedge marked ΑΒΓ, and the object being wedged ΔΕΗΖ. Now, ΑΒ becomes a lever, the weight being the part of Β from below, and the fulcrum being ΖΔ. The lever opposed to this is ΒΓ. And ΑΓ, being struck, uses each of these as a lever; for it pries up Β.

Notes

17.1ὃ καὶ ἀνασπᾷ ἢ πιέζει — The relative pronoun ὃ takes the preceding ἑκάτερος (each, here treated in the neuter or representing the general force of each lever) as its antecedent, describing the action of prying up or pressing down that each lever performs.
17.1ἡ τῆς πληγῆς φορὰ τὸ βάρος, ὃ τύπτει καὶ κινεῖ, ποιεῖ μέγα — Syntactically, ἡ τῆς πληγῆς φορὰ is the subject, ποιεῖ is the main verb, τὸ βάρος is the object, and μέγα is the object complement, with the relative clause ὃ τύπτει καὶ κινεῖ modifying τὸ βάρος. It means 'the momentum of the blow makes the weight, which strikes and moves, great.'
17.1διὰ τὸ κινούμενον κινεῖν — This is an articular infinitive construction (τὸ ... κινεῖν) governed by the preposition διὰ. The present passive participle κινούμενον (that which is set in motion / in motion) functions as the accusative subject of the infinitive κινεῖν.
17.2λανθάνει κινῶν — The verb λανθάνω combined with the present participle κινῶν (from κινέω) forms an idiomatic construction meaning 'to do something unnoticed'. Here it means 'it escapes notice that it moves [something] out of proportion to its size.'
17.2ἑκατέρᾳ τούτων χρῆται μοχλῷ — The object of the verb χρῆται (from χράομαι, which governs the dative) is ἑκατέρᾳ τούτων (each of these two, i.e., lines ΑΒ and ΒΓ) in the dative, while μοχλῷ functions as a predicative dative meaning 'as a lever'.

Cite this passage

Aristotle, Mechanics §17.1-17.2. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg023.humanitext-grc1:17.1-17.2

Please note the AI-draft status of the translation and the date accessed.

Translation, notes and summary are AI-generated drafts, revised through reader feedback.