Humanitext Reader

Aristotle · Mechanics §29.1-29.2

Why an Off-Center Load on a Pole Is Shared Unevenly

Passage 32 of 38 · Greek

Summary

This section explains why the load is unevenly distributed when two people carry a weight on a pole not in the middle, analyzing it through the principle of the lever by casting the pole as the lever, the weight as the fulcrum, and the carriers as the mover and the weight to be moved.

§29.1Διὰ τί, ὅταν φέρωσιν ἐπὶ ξύλου ἤ τινος τοιούτου δύο ἄνθρωποι ἴσον βάρος, οὐχ ὁμοίως θλίβονται, ἐὰν μὴ ἐπὶ τῷ μέσῳ ᾖ τὸ βάρος, ἀλλὰ μᾶλλον ὅσῳ ἄν ἐγγύτερον ᾖ τῶν φερόντων;
Why is it that, when two men carry an equal weight on a piece of wood or something of the sort, they are not pressed upon equally if the weight is not in the middle, but rather the closer it is to one of the carriers, the more that person is pressed?
Ἥ διότι μοχλὸς μὲν γίνεταιοὕτως ἐχόντωντὸ ξύλον, τὸ δὲ βάρος ὑπομόχλιον, ὁ δὲ ἐγγύτερος τοῦ βάρους τῶν φερόντων τὸ βάρος τὸ κινούμενον, ἄτερος δὲ τῶν φερόντων τὸ βάρος ὁ κινῶν.
Or is it because, when things are thus, the wood becomes a lever, the weight the fulcrum, the one of the carriers who is closer to the weight becomes the weight to be moved, and the other of the carriers becomes the mover?
§29.2Ὄσῳ γὰρ πλέον ἀπέχει τοῦ βάρους,τοσούτῳ ῥᾷον κινεῖ, καὶ θλίβει μᾶλλον τὸν ἕτερον εἰς τὸ κάτω, ὥσπερ ἀντερείδοντος τοῦ βάρους τοῦ ἐπικειμένου καὶ γινομένου ὑπομοχλίου.
For the further he is from the weight, the more easily he moves it, and the more he presses the other downward, as if the weight placed upon them were resisting and becoming a fulcrum.
Ἐν μέσῳ δὲ ὑποκειμένου τοῦ βάρους, οὐδὲν μᾶλλον ἅτερος θατέρῳ γίνεται βάρος, οὐδὲ κινεῖ, ἀλλ’ ὁμοίως ἑκάτερος ἑκατέρῳ γίνεται βάρος.
But when the weight is placed in the middle, neither of them becomes a weight to the other, nor does he move him, but each becomes a weight to the other equally.

Notes

  1. §29.1οὕτως ἐχόντων — The participle ἐχόντων is a genitive absolute construction with its third-person plural subject omitted, or used impersonally to mean 'things being in this state.'
  2. §29.1ἄτερος δὲ τῶν φερόντων τὸ βάρος ὁ κινῶν — The copula (γίνεται) is omitted. The subject is ἄτερος τῶν φερόντων (the other of the carriers) and the predicate is ὁ κινῶν (the mover). ἄτερος is a crasis of the article ὁ and ἕτερος (ὁ ἕτερος > ἅτερος).
  3. §29.2ὥσπερ ἀντερείδοντος τοῦ βάρους — The conjunction ὥσπερ is combined with the genitive absolute (split as ἀντερείδοντος τοῦ βάρους...) to express a hypothetical or metaphorical situation: 'as if the weight placed upon them were resisting and becoming a fulcrum.'
  4. §29.2ὑποκειμένου τοῦ βάρους — This is a genitive absolute construction expressing a condition ('when/if the weight is placed in the middle'), serving as a contrast to the previous uneven scenario where the lever principle applies.

Cite this passage

Aristotle, Mechanics §29.1-29.2. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg023.humanitext-grc1:29.1-29.2

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