Pappus Alexandrinus, Mathematical Collection, Book 8, 1876

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    <archimedes>
      <text>
        <body>
          <chap>
            <p>
              <s id="id.000280">
                <pb n="1110"/>
              </s>
            </p>
            <p>
              <s id="id.000281">Νοείσθω κύλινδρος ἰσοπαχῶς τετορνευμένος ὁ ΑΔΕΖ,
                <lb n="1"/>
              πλευρὰ δ' αὐτοῦ ἡ ΑΕ, καὶ εἰλήφθω μονοστρόφου ἕλικος
                <lb n="2"/>
              ἐπ' αὐτῆς διάστημα τὸ ΑΒ, καὶ λεπίδιον χαλκοῦν γεγενή-
                <lb n="3"/>
              σθω, οὗ τὸ μὲν ΗΘΚ μέρος τρίγωνον ὀρθογώνιον ἔστω
                <lb n="4"/>
              ὀρθὴν ἔχον τὴν Θ γωνίαν, τὸ δὲ λοιπὸν παραλληλόγραμμον
                <lb n="5"/>
              ὀρθογώνιον τὸ ΘΚΛ, ἴση δὲ κείσθω ἡ ΘΗ τῇ ΑΒ, ἡ δὲ
                <lb n="6"/>
              ΘΚ τῇ περιμέτρῳ τοῦ ΑΔΕΖ κυλίνδρου, καὶ περικαμπτέ-
                <lb n="7"/>
              σθω τὸ λεπίδιον περὶ τὸν κύλινδρον, ἵνα καὶ τὸ ΘΚΛ
                <lb n="8"/>
              παραλληλόγραμμον κύλινδρος γένηται ἁπτόμενος τοῦ ΔΕ,
                <lb n="9"/>
              ὅταν εἰσαχθῇ, καὶ κείσθω τὸ μὲν Θ ἐπὶ τὸ Α, τὸ δὲ Η
                <lb n="10"/>
              ἐπὶ τὸ Β, καὶ οὕτως γράψομεν διὰ τῆς ΗΚ ὑποτεινούσης
                <lb n="11"/>
              καμφθείσης [δὲ] τὴν καλουμένην μονόστροφον ἕλικα ὡς τὴν
                <lb n="12"/>
              ΒΑ. </s>
              <s id="id.000282">καὶ πάλιν μεταθέντες τὸ λεπίδιον, ὥστε τὸ μὲν Θ
                <lb n="13"/>
              κατὰ τὸ Β εἶναι τὸ δὲ Η κατὰ τὸ Γ, γράψομεν διὰ τῆς
                <lb n="14"/>
              ΗΚ ἑτέραν ἕλικα μονόστροφον, ὥστε τὴν ὅλην εἶναι δί-
                <lb n="15"/>
              στροφον. </s>
              <s id="id.000283">ἐν ᾧ γὰρ χρόνῳ τὸ Α ἐπὶ τὸ Β παραγίνεται
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              ὁμαλῶς κινούμενον, ἐν τούτῳ καὶ ἡ ΑΒ κατὰ τῆς ἐπιφα-
                <lb n="17"/>
              νείας τοῦ κυλίνδρου κινηθεῖσα εἰς τὸ αὐτὸ ἀποκαθίσταται
                <lb n="18"/>
              καὶ τὸ εἰρημένον φέρεσθαι σημεῖον κατὰ τῆς ΑΒ εὐθείας
                <lb n="19"/>
              γράψει τὴν μονόστροφον ἕλικα· τοῦτο γὰρ Ἀπολλώνιος ὁ
                <lb n="20"/>
              Περγεὺς ἀπέδειξεν. </s>
              <s id="id.000284">[ἐὰν οὖν καὶ ἑκατέραν τῶν ΑΒ ΒΓ
                <lb n="21"/>
              καὶ τὰς ἑξῆς ἄχρι τοῦ Ε δίχα τέμνωμεν καὶ διὰ τῶν ση-
                <lb n="22"/>
              μείων τῷ λεπιδίῳ γράψωμεν μονοστρόφους ἕλικας ἀπ' αὐτῶν
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              κατὰ τὸ βάθος τῆς ἕλικος ὃ βουλόμεθα λάβωμεν καὶ ἀπὸ
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              τοῦ βάθους λοιπὸν καὶ τῆς γραφείσης ἕλικος, ῥᾳδίως τὴν
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              ἕλικα φακοειδῆ ῥινήσαντες ἕξομεν ἀπηρτισμένην.]
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              </s>
            </p>
            <p>
              <s id="id.000285">κθ#. </s>
              <s id="id.000286">Πάλιν νοείσθω ἐν τῇ ἑτέρᾳ ἐπιφανείᾳ τοῦ δοθέν-
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              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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