Pappus Alexandrinus, Mathematical Collection, Book 8, 1876

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    <archimedes>
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        <body>
          <chap>
            <p>
              <s id="id.000033">
                <pb n="1034"/>
              </s>
            </p>
            <p>
              <s id="id.000034">Τὸ μὲν οὖν μάλιστα συνέχον τὴν κεντροβαρικὴν πραγ-
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              ματείαν τοῦτ' ἂν εἴη, μάθοις δ' ἂν τὰ μὲν στοιχειώδη
                <lb n="2"/>
              ὄντα διὰ ταύτης δεικνύμενα τοῖς Ἀρχιμήδους περὶ ἰσορ-
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              ροπιῶν ἐντυχὼν καὶ τοῖς Ἥρωνος μηχανικοῖς, ὅσα δὲ
                <lb n="4"/>
              μὴ γνώριμα τοῖς πολλοῖς γράψομεν ἐφεξῆς, οἷον τὰ τοι-
                <lb n="5"/>
              αῦτα.
                <lb n="6"/>
              </s>
            </p>
            <p>
              <s id="id.000035">γ#. </s>
              <s id="id.000036">Ἔστω τρίγωνον τὸ ΑΒΓ, καὶ αἱ πλευραὶ αὐτοῦ εἰς
                <lb n="7"/>
              τὸν αὐτὸν λόγον τεμνέσθωσαν τοῖς Η Θ Κ σημείοις, ὥστε
                <lb n="8"/>
              εἶναι ὡσ τὴν ΑΗ πρὸς ΗΒ, τὴν ΒΘ πρὸς ΘΓ καὶ τὴν ΓΚ
                <lb n="9"/>
              πρὸς ΚΑ, καὶ ἐπεζεύχθωσαν αἱ ΗΘ ΘΚ ΚΗ· ὅτι τοῦ ΑΒΓ
                <lb n="10"/>
              τριγώνου καὶ τοῦ ΗΘΚ τὸ αὐτὸ κέντρον τοῦ βάρους ἐστίν.
                <lb n="11"/>
              </s>
            </p>
            <p>
              <s id="id.000037">Τετμήσθωσαν γὰρ αἱ ΒΓ ΓΑ δίχα τοῖς Δ Ε, καὶ
                <lb n="12"/>
              ἐπεζεύχθωσαν αἱ ΑΔ ΒΕ· τὸ Ζ ἄρα κέντρον βάρους ἐστὶν
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              τοῦ ΑΒΓ τριγώνου. </s>
              <s id="id.000038">ἐὰν γὰρ τὸ τρίγωνον ἐπί τινος ὀρθοῦ
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              ἐπιπέδου ἐπισταθῇ κατὰ τὴν ΑΔ εὐθεῖαν, ἐπ' οὐδέτερον
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              μέρος ῥέψει τὸ τρίγωνον διὰ τὸ ἴσον εἶναι τὸ ΑΒΔ τρί-
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              γωνον τῷ ΑΓΔ τριγώνῳ. </s>
              <s id="id.000039">ἐπισταθὲν δὲ ὁμοίως τὸ ΑΒΓ
                <lb n="17"/>
              τρίγωνον κατὰ τὴν ΒΕ ἐπὶ τοῦ ὀρθοῦ ἐπιπέδου ἐπ' οὐ-
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              δέτερον μέρος ῥέψει διὰ τὸ ἴσα εἶναι τὰ ΑΒΕ ΒΓΕ τρί-
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              γωνα. </s>
              <s id="id.000040">εἰ δὲ ἐφ' ἑκατέρας τῶν ΑΔ ΒΕ ἰσορροπεῖ τὸ
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              τρίγωνον, τὸ ἄρα κοινὸν αὐτῶν σημεῖον τὸ Ζ κέντρον ἔσται
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              τοῦ βάρους. </s>
              <s id="id.000041">[νοεῖν δὲ δεῖ τὸ Ζ, ὡς προείρηται, κείμενον
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              ἐν μέσῳ τοῦ ΑΒΓ τριγώνου ἰσοπαχοῦς τε καὶ ἰσοβαροῦς δη-
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              λονότι ὑποκειμένου.]</s>
              <s id="id.000042"> καὶ φανερὸν ὅτι διπλασία ἐστὶν ἡ
                <lb n="24"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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