Heron Alexandrinus, Mechanicorum Fragmenta, 1899

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      <text>
        <body>
          <chap n="1">
            <p n="11">
              <s id="id.000029">
                <pb pagenum="270"/>
              </s>
              <s id="id.000030">Ἐπεὶ γὰρ ὀρθογώνιόν ἐστιν τὸ ΑΒΓΔ παραλληλό­
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              γραμμον, αἱ τέσσαρες εὐθεῖαι αἱ ΔΗ, ΗΑ, ΗΒ, ΗΓ
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              ἴσαι ἀλλήλαις εἰσίν. </s>
              <s id="id.000031">ἐπεὶ οὖν ἴση ἡ ΔΗ τῇ ΑΗ καὶ
                <lb n="21"/>
              διῆκται ἡ ΗΖ, τὸ ἄρα ὑπὸ ΔΖΑ μετὰ τοῦ ἀπὸ ΑΗ
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              ἴσον ἐστὶν τῷ ἀπὸ ΗΖ. </s>
              <s id="id.000032">διὰ τὰ αὐτὰ δὴ καὶ τὸ ὑπὸ
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              ΔΕΓ μετὰ τοῦ ἀπὸ ΓΗ ἴσον ἐστὶν τῷ ἀπὸ ΗΕ.
                <lb n="24"/>
              </s>
              <s id="id.000033">ἴσον ἄρα καὶ τὸ ὑπὸ
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              ΔΖΑ μετὰ τοῦ ἀπὸ ΑΗ τῷ ὑπὸ ΔΕΓ μετὰ τοῦ ἀπὸ
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              ΓΗ. </s>
              <s id="id.000034">λοιπὸν
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              ἄρα τὸ ὑπὸ ΔΕΓ ἴσον ἐστὶν τῷ ὑπὸ ΔΖΑ. </s>
              <s id="id.000035">ὡς ἄρα
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              ἡ ΕΔ πρὸς ΔΖ, ἡ ΖΑ πρὸς ΓΕ. </s>
              <s id="id.000036">ὡς δὲ ἡ ΕΔ πρὸς
                <lb n="29"/>
              ΔΖ, ἥ τε ΒΑ πρὸς ΑΖ καὶ ἡ ΕΓ πρὸς ΓΒ, ὥστε
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              ἔσται καὶ ὡς ἡ ΑΒ πρὸς ΑΖ, ἥ τε ΖΑ πρὸς ΓΕ καὶ
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              ἡ ΓΕ πρὸς ΓΒ. </s>
              <s id="id.000037">τῶν ἄρα ΑΒ, ΒΓ μέσαι ἀνάλογόν
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              εἰσιν αἱ ΑΖ, ΓΕ.
                <lb n="33"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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