Humanitext Reader

Aristotle · Mechanics §30.1-30.4

Why One Must Bend to Acute Angles to Stand Up

Passage 33 of 38 · Greek

Summary

The author explains why anyone who stands up must bend their knees and chest to form acute angles, bringing the head over the feet, through the physical and geometrical relationship between perpendicularity and stability.

§30.1Διὰ τί οἱ ἀνιστάμενοι πάντες πρὸς ὀξεῖαν γωνίαν τῷ μηρῷ ποιήσαντες τὴν κνήμην ἀνίστανται, καὶ τῷ θώρακι πρὸς τὸν μηρόν;
Why is it that all who stand up do so by making an acute angle of the shin with the thigh, and of the chest with the thigh?
εἰ δὲ μή, οὐκ ἂν δύναιντο ἀναστῆναι.
Otherwise, they would not be able to stand up.
Πότερον ὅτι τὸ ἴσον ἠρεμίας πανταχοῦ αἴτιον, ἡ δὲ ὀρθὴ γωνία τοῦ ἴσου, καὶ ποιεῖ στάσιν· διὸ καὶ φέρεται πρὸς ὁμοίας γωνίας τῇ περιφερείᾳ τῆς γῆς.
Is it because equality is everywhere the cause of rest, and the right angle belongs to equality and produces stability; which is why also [a falling body] is carried at similar angles to the circumference of the earth?
§30.2Οὐ γὰρ ὅτι καὶ πρὸς ὀρθὴν ἔσται τῷ ἐπιπέδῳ.
For it is not because it will also be at right angles to the plane.
Ἣ ὅτι ἀνιστάμενος γίνεται ὀρθός, ἀνάγκη δὲ τὸν ἑστῶτακάθετον εἶναι πρὸς τὴν γῆν.
Or is it because he who stands up becomes upright, and it is necessary for the standing person to be perpendicular to the earth?
Εἰ οὖν μέλλει ἔσεσθαι πρὸς ὁρθήν, τοῦτο δέ ἐστι τὸ τὴν κεφαλὴν ἔχειν κατὰ τοὺς πόδας, καὶ γίνεσθαι δὴ ὅτε ἀνίσταται.
If, then, he is to be at right angles, and this consists in having the head vertically above the feet, which indeed happens when he stands up.
Ὄταν μὲν οὖν καθήμενος ᾖ, παράλληλον ἔχει τὴν κεφαλὴν καὶ τοὺς πόδας, καὶ οὐκ ἐπὶ μιᾶςεὐθείας.
Now, when he is sitting, he has his head and feet parallel, and not on one straight line.
§30.3Ἡ κεφαλὴ Α ἔστω, θώραξ Α Β, μόρος Β Γ, κνήμη Γ Δ. Πρὸς ὀρθὴν δὲ γίνεται ὅ τε θώραξ [ἐφ’ ὦν Α Β] τῷ μηρῷ καὶ ὁ μηρὸς τῇ κνήνμη οὕτως καθημένῳ.
Let A be the head, AB the chest, BC the thigh, CD the shin. For a person sitting in this way, both the chest [AB] is at right angles to the thigh, and the thigh to the shin.
Ὤστε οὕτως ἔχοντα ἀδύνατον ἀναστῆναι.
So that, being in this posture, it is impossible to stand up.
Ἀνάγκη δὲ ἐγκλῖναι τὴν κνήμην καὶ ποιεῖν τοὺς πόδας ὑπὸ τὴν κεφαλήν.
But it is necessary to bend the shin and bring the feet under the head.
§30.4Τοῦτο δὲ ἔσται, ἐὰν ὁ Γ Δ ἐφ’ ἦς τὰ Γ Ζ γένηται, καὶ ἅμα ἀναστῆναι συμβήσεται, καὶ ἔχειν ἐπὶ τῆς αὐτῆς ἴσης τὴν κεφαλήν τε καὶ τοὺς πόδας.
And this will happen if CD becomes GZ, and at the same time it will happen that he stands up and has both his head and feet on the same equal [straight line].
Ἡ δὲ Γ Ζ ὀξεῖαν ποιεῖ γωνίαν πρὸς τὴν Β Γ.
And GZ makes an acute angle with BC.

Notes

  1. §30.1πρὸς ὀξεῖαν γωνίαν τῷ μηρῷ ποιήσαντες τὴν κνήμην — The participle ποιήσαντες (aorist active) expresses means. πρὸς ὀξεῖαν γωνίαν represents the resulting state ('to an acute angle'), while the dative τῷ μηρῷ is a dative of relation ('with respect to the thigh') modifying the phrase, with τὴν κνήμην serving as the accusative direct object.
  2. §30.2τοῦτο δέ ἐστι τὸ τὴν κεφαλὴν ἔχειν κατὰ τοὺς πόδας — The demonstrative pronoun τοῦτο is explained by the articular infinitive phrase τὸ ... ἔχειν functioning as a predicate nominative. The direct object of the infinitive ἔχειν is the accusative τὴν κεφαλὴν, with its subject (the person standing) understood from the context. The preposition κατὰ indicates vertical alignment ('in line with' or 'vertically above').
  3. §30.4ἐπὶ τῆς αὐτῆς ἴσης — While some manuscripts read εὐθείας (straight line) instead of ἴσης, the text's ἴσης (equal [line]) refers to being on the same reference line that maintains an equal or balanced perpendicular relation. It is a feminine genitive adjective agreeing with an implied feminine noun γραμμῆς (line).

Cite this passage

Aristotle, Mechanics §30.1-30.4. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg023.humanitext-grc1:30.1-30.4

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