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Aristotle · Mechanics §9.1

Why Larger Circles and Pulleys Move Loads More Easily

Passage 11 of 38 · Greek

Summary

Addressing the question of why larger circles (pulleys or rollers) make it easier and faster to move objects, the text explains this by applying the principle of the balance, noting that a longer radius covers a greater distance in the same amount of time.

§9.1Διὰ τί τὰ διὰ τῶν μειζόνων κύκλων αἰρόμενα καὶ ἑλκόμενα ῥᾷον καὶ θᾶττον κινοῦμεν;
Why is it that we move things that are raised and dragged by means of larger circles more easily and quickly?
οἷον καὶ αἱ τροχιλέαι αἱ μείζους τῶν ἐλαττόνων, καὶ αἱ σκυτάλαι ὁμοίως.
As is the case with larger pulleys compared to smaller ones, and likewise with rollers.
Ἤ διότι ὅσῳ ἂν μείζων· ἡ ἐκ τοῦ κέντρουᾖ, ἐν τῷ ἴσῳχρόνῳ πλέον κινεῖται χωρίον, ὥστε καὶ τοῦ ἴσον βάρους ἐπόντος ποιήσει τὸ αὐτό, ὥσπερ εἴπομεν καὶ τὰ μείζω ζυγὰ τῶν ἐλαττόνωνἀκριβέστερα εἶναι.
Or is it because the larger the line from the center is, the greater is the distance it moves in an equal time, so that even when an equal weight is upon it, it will produce the same effect, just as we said that larger balances are more accurate than smaller ones?
Τὸ μὲν γὰρ σπαρτίον ἐστὶ κέντρον, τοῦ δὲ ζυγοῦ αἱ ἐπὶ τάδε τοῦ σπαρτίου αἱ ἐκ τοῦ κέντρου.
For the cord is the center, and the parts of the balance on this side of the cord are the lines from the center.

Notes

  1. §9.1ἡ ἐκ τοῦ κέντρου — The feminine singular article `ἡ` implies the omission of the noun `γραμμή` (line), forming a geometrical idiom meaning 'the line from the center', i.e., 'the radius'.
  2. §9.1τοῦ ἴσου βάρους ἐπόντος — A genitive absolute construction consisting of the noun `βάρους` and the participle `ἐπόντος` (from `ἔπειμι`, 'to be upon'), here expressing a concessive meaning ('even when...').
  3. §9.1αἱ ἐπὶ τάδε — The feminine plural article `αἱ` refers to the implied 'arms' or 'parts' of the balance, substantivizing the prepositional phrase `ἐπὶ τάδε` ('on this side').

Cite this passage

Aristotle, Mechanics §9.1. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg023.humanitext-grc1:9.1

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