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Aristotle · Mechanics §13.1-13.2

Why Larger Pegs and Thinner Windlasses Turn More Easily

Passage 15 of 38 · Greek

Summary

This section explains why larger pegs and thinner windlasses are moved more easily around the same axis, attributing it to the mechanical principle that a greater radius from the center facilitates faster and larger movement under the same force.

§13.1Διὰ τί ῥᾷον κινοῦνται περὶ τὸ αὐτὸ ζυγὸν οἱ μείζους τῶν ἐλαττόνων κόλλοπες, καὶ οἱ αὐτοὶ ὄνοι οἱ λεπτότεροι ὑπὸ τῆς αὐτῆς ἰσχύος τῶν παχυτέρων;
Why are larger pegs moved more easily than smaller ones around the same yoke, and, by the same force, thinner windlasses more easily than thicker ones?
Ἣ διότι ὁ μὲν ὅνος καὶ τὸ ζυγὸν κέντρον ἐστίν, τὰ δὲἀπέχοντα μεγέθη αἱ ἐκ τοῦ κέντρου;
Or is it because the windlass and the yoke are the center, and the distances extending from them are the lines from the center?
§13.2Θᾶττον δὲ κινοῦνται καὶ πλέον ἀπὸ τῆςαὐτῆς ἰσχύος αἱ τῶν μειζόνων κύκλων ἢ αἱ τῶν ἐλαττόνων· ὑπὸ τῆς αὐτῆς γὰρ ἰσχύοςθᾶττον μεθίσταται τὸ ἄκρον τὸ πορρώτερον τοῦ κέντρου.
And the lines of larger circles are moved faster and further by the same force than those of smaller ones; for under the same force, the extremity which is further from the center is displaced more quickly.
Διὸ πρὸς μὲν τὸ ζυγὸν τοὺς κόλλοπας ὄργανα ποιοῦνται, οἶς ῥᾷον στρέφουσιν· ἐν δὲ τοῖς λεπτοῖς ὄνοις πλεῖον γίνεται τὸ ἔξω τοῦ ξύλου, αὕτη δὲ γίνεται ἡ ἐκ τοῦ κέντρου.
Therefore, they make the pegs into instruments for the yoke, by which they turn it more easily; and in the case of thin windlasses, the portion outside the wood becomes greater, and this becomes the line from the center.

Notes

  1. §13.1αἱ ἐκ τοῦ κέντρου — The feminine plural article αἱ implies the omission of γραμμαί (lines), meaning "the lines from the center" (radii) in a geometrical context.
  2. §13.2τοὺς κόλλοπας ὄργανα ποιοῦνται — A double accusative construction where τοὺς κόλλοπας is the direct object and ὄργανα is the predicative complement, meaning "they make the pegs into instruments."
  3. §13.2τὸ ἔξω τοῦ ξύλου — An attributive neuter singular phrase with a genitive, referring to "the part outside the wood," meaning the protruding length of the handle or lever beyond the windlass drum.

Cite this passage

Aristotle, Mechanics §13.1-13.2. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg023.humanitext-grc1:13.1-13.2

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