Pappus Alexandrinus, Mathematical Collection, Book 8, 1876

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    <archimedes>
      <text>
        <body>
          <chap>
            <p>
              <s id="id.000267">
                <pb n="1106"/>
              </s>
            </p>
            <p>
              <s id="id.000268">Ἔστωσαν γὰρ δύο κύκλοι οἱ ΑΒ ΓΔ, καὶ διάμετροι
                <lb n="1"/>
              αὐτῶν αἱ ΑΒ ΓΔ· λέγω ὅτι ἐστὶν ὡς ἡ τοῦ ΑΒ κύκλου
                <lb n="2"/>
              περιφέρεια πρὸς τὴν τοῦ ΓΔ κύκλου περιφέρειαν, οὕτως ἡ
                <lb n="3"/>
              ΑΒ διάμετρος πρὸς τὴν ΓΔ.
                <lb n="4"/>
              </s>
            </p>
            <p>
              <s id="id.000269">Ἐπεὶ γάρ ἐστιν ὡς ὁ ΑΒ κύκλος πρὸς τὸν ΓΔ κύκλον,
                <lb n="5"/>
              οὕτως τὸ ἀπὸ τῆς ΑΒ τετράγωνον πρὸς τὸ ἀπὸ τῆς ΓΔ
                <lb n="6"/>
              τετράγωνον, ἀλλὰ τοῦ μὲν ΑΒ κύκλου τετραπλάσιόν ἐστιν
                <lb n="7"/>
              τὸ περιεχόμενον ὀρθογώνιον ὑπό τε τῆς ΑΒ διαμέτρου καὶ
                <lb n="8"/>
              τῆς τοῦ ΑΒ περιφερείας, τοῦ δὲ ΓΔ κύκλου τετραπλάσιόν
                <lb n="9"/>
              ἐστιν τὸ ὑπὸ τῆς ΓΔ καὶ τῆς τοῦ ΓΔ περιφερείας [1τὸ γὰρ
                <lb n="10"/>
              ὑπὸ τῆς ἐκ τοῦ κέντρου τοῦ κύκλου καὶ τῆς περιμέτρου τοῦ
                <lb n="11"/>
              κύκλου περιεχόμενον ὀρθογώνιον διπλάσιόν ἐστιν τοῦ ἐμ-
                <lb n="12"/>
              βαδοῦ τοῦ κύκλου, ὡς Ἀρχιμήδης, καὶ ὡς ἐν τῷ εἰς τὸ
                <lb n="13"/>
              πρῶτον τῶν μαθηματικῶν σχολίῳ δέδεικται καὶ ὑφ' ἡμῶν
                <lb n="14"/>
              δι' ἑνὸς θεωρήματοσ]1, καὶ ὡς ἄρα τὸ ὑπὸ τῆς ΑΒ καὶ τῆς
                <lb n="15"/>
              περιφερείας τοῦ ΑΒ πρὸς τὸ ὑπὸ τῆς ΓΔ καὶ τῆς τοῦ ΓΔ
                <lb n="16"/>
              κύκλου περιφερείας, οὕτως τὸ ἀπὸ τῆς ΑΒ τετράγωνον
                <lb n="17"/>
              πρὸς τὸ ἀπὸ τῆς ΓΔ. </s>
              <s id="id.000270">καὶ ἐναλλὰξ ὡς τὸ ὑπὸ τῆς τοῦ ΑΒ
                <lb n="18"/>
              κύκλου περιφερείας καὶ τῆς ΑΒ πρὸς τὸ ἀπὸ τῆς ΑΒ,
                <lb n="19"/>
              οὕτως τὸ ὑπὸ τῆς τοῦ ΓΔ κύκλου περιφερείας καὶ τῆς ΓΔ
                <lb n="20"/>
              πρὸς τὸ ἀπὸ τῆς ΓΔ· καὶ ὡς ἄρα ἡ τοῦ ΑΒ κύκλου πε-
                <lb n="21"/>
              ριφέρεια πρὸς τὴν ΑΒ, οὕτως ἡ τοῦ ΓΔ περιφέρεια πρὸς τὴν
                <lb n="22"/>
              ΓΔ [1τοῦτο γὰρ πρῶτόν ἐστιν ἐν τῷ ς# λαμβανόμενον]1, καὶ
                <lb n="23"/>
              ἐναλλὰξ ὡς ἡ τοῦ ΑΒ περιφέρεια πρὸς τὴν τοῦ ΓΔ περι-
                <lb n="24"/>
              φέρειαν, οὕτως ἡ ΑΒ πρὸς τὴν ΓΔ.
                <lb n="25"/>
              </s>
            </p>
            <p>
              <s id="id.000271">κζ#. </s>
              <s id="id.000272">Τυμπάνου δοθέντος καὶ τοῦ πλήθους τῶν ὀδόντων
                <lb n="26"/>
              αὐτοῦ, ἐπιτετάχθω παραθεῖναι αὐτῷ τύμπανον δοθὲν ἔχον
                <lb n="27"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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