Aristotle, Problemata Mechanika, 1831

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            <p n="44">
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              ἓξ ποδῶν καὶ μικρῷ μείζω πλευράν, τὴν δὲ τριῶν; καὶ
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              διὰ τί ἐντείνουσιν οὐ κατὰ διάμετρον; </s>
              <s id="g0132502">ἢ τὸ μὲν μέγεθος τηλικαύτας,
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              ὅπως τοῖς σώμασιν ὦσι σύμμετροι; γίνονται
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              γὰρ οὕτω διπλασιόπλευροι, τετραπήχεις μὲν τὸ μῆκος, διπήχεις
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              δὲ τὸ πλάτος.</s>
              <s id="g0132503">ἐντείνουσι δὲ οὐ κατὰ διάμετρον ἀλλ'
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              ἀπ' ἐναντίας, ὅπως τά τε ξύλα ἧττον διασπᾶται· τάχιστα
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              γὰρ σχίζεται κατὰ φύσιν διαιρούμενα ταύτῃ, καὶ ἑλκόμενα
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              πονεῖ μάλιστα.</s>
              <s id="g0132504">ἔτι ἐπειδὴ δεῖ βάρος δύνασθαι τὰ
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              σπαρτία φέρειν, οὕτως ἧττον πονέσει λοξοῖς τοῖς σπαρτίοις
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              ἐπιτιθεμένου τοῦ βάρους ἢ πλαγίοις.</s>
              <s id="g0132505">ἔτι δὲ ἔλαττον οὕτω
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              σπαρτίον ἀναλίσκεται.</s>
              <s id="g0132506">ἔστω γὰρ κλίνη ἡ ΑΖΗΙ, καὶ δίχα
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              διῃρήσθω ἡ ΖΗ κατὰ τὸ Β. ἴσα δὴ τρυπήματά ἐστιν
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              ἐν τῇ ΖΒ καὶ ἐν τῇ ΖΑ. καὶ γὰρ αἱ πλευραὶ ἴσαι εἰσίν·
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              ἡ γὰρ ὅλη ΖΗ διπλασία ἐστίν.</s>
              <s id="g0132507">ἐντείνουσι δ' ὡς γέγραπται,
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              ἀπὸ τοῦ Α ἐπὶ τὸ Β, εἶτα οὗ τὸ Γ, εἶτα οὗ τὸ Δ, εἶτα οὗ
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              τὸ Θ, εἶτα οὗ τὸ Ε. καὶ οὕτως ἀεί, ἕως ἂν εἰς γωνίαν
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              καταστρέψωσιν ἄλλην· </s>
              <figure id="id.080.01.020.1.jpg" xlink:href="080/01/020/1.jpg" number="21"/>
              <s id="g0132508">δύο γὰρ ἔχουσι γωνίαι τὰς ἀρχὰς
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              τοῦ σπαρτίου.</s>
              <s id="g0132509">ἴσα δέ ἐστι τὰ σπαρτία κατὰ τὰς κάμψεις,
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              τό τε ΑΒ καὶ ΒΓ τῷ ΓΔ καὶ ΔΘ. καὶ τὰ ἄλλα δὲ
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              τὰ τοιαῦτά ἐστιν, ὅτι οὕτως ἔχει ἡ αὐτὴ ἀπόδειξις.</s>
              <s id="g0132510">ἡ μὲν
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              γὰρ ΑΒ τῇ ΕΘ ἴση· ἴσαι γάρ εἰσιν αἱ πλευραὶ τοῦ ΒΗΚ
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              Α χωρίου, καὶ τὰ τρυπήματα ἴσα διέστηκεν.</s>
              <s id="g0132511">ἡ δὲ ΒΗ ἴση
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              τῇ ΚΑ· ἡ γὰρ Β γωνία ἴση τῇ Η. ἐν ἴσοις γὰρ ἡ μὲν
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              ἐκτός, ἡ δὲ ἐντός· καὶ ἡ μὲν Β ἐστὶν ἡμίσεια ὀρθῆς· ἡ
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              γὰρ ΖΒ ἴση τῇ ΖΑ· καὶ γωνία δὲ ἡ κατὰ τὸ Ζ ὀρθή.</s>
              <s id="g0132512">ἡ
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              δὲ Β γωνία ἴση τῇ κατὰ τὸ Η· ἡ γὰρ κατὰ τὸ Ζ ὀρθή,
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              ἐπειδὴ διπλασιόπλευρον τὸ ἑτερόμηκες καὶ πρὸς μέσον κέκλασται.
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              ὥστε ἡ ΑΓ τῇ ΕΗ ἴση. ταύτῃ δὲ ἡ ΚΘ· παράλληλος
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              γάρ. ὥστε ἡ ΒΓ ἴση τῇ ΚΘ. ἡ δὲ ΓΕ τῇ ΔΘ.</s>
              <s id="g0132513">
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              ὁμοίως δὲ καὶ αἱ ἄλλαι δείκνυνται ὅτι ἴσαι εἰσὶν αἱ κατὰ
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              τὰς κάμψεις δύο ταῖς δυσίν.</s>
              <s id="g0132514">ὥστε δῆλον ὅτι τὰ τηλικαῦτα
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              σπαρτία ὅσον τὸ ΑΒ, τέσσαρα τοσαῦτ' ἔνεστιν ἐν τῇ κλίνῃ· </s>
              <s id="g0132515">
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              ὅσον δ' ἐστὶ τὸ πλῆθος τῶν ἐν τῇ ΖΗ πλευρᾷ τρυπημάτων,
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              καὶ ἐν τῷ ἡμίσει τῷ ΖΒ τὰ ἡμίση.</s>
              <s id="g0132516">ὥστε ἐν τῇ ἡμισείᾳ
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              κλίνῃ τηλικαῦτα μεγέθη σπαρτίων ἐστὶν ὅσον τῷ ΒΑ ἔνεστι,
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              τοσαῦτα δὲ τὸ πλῆθος ὅσαπερ ἐν τῷ ΒΗ τρυπήματα.</s>
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              ταῦτα δὲ οὐδὲν διαφέρει λέγειν ἢ ὅσα ἐν τῇ ΑΖ καὶ ΒΖ
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              τὰ συνάμφω.</s>
              <figure id="id.080.01.020.2.jpg" xlink:href="080/01/020/2.jpg" number="22"/>
              <s id="g0132518">εἰ δὲ κατὰ διάμετρον ἐνταθῇ τὰ σπαρτία,
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              ὡς ἐν τῇ ΑΒΓΔ κλίνῃ ἔχει, τὰ ἡμίσεά εἰσιν οὐ τοσαῦτα</s>
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