Pappus Alexandrinus, Mathematical Collection, Book 8, 1876

Table of figures

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      <text>
        <body>
          <chap>
            <p>
              <s id="id.000223">
                <pb n="1096"/>
              </s>
            </p>
            <p>
              <s id="id.000224">Κείσθω γὰρ ἡ σφαῖρα περὶ κέντρον τὸ Β, καὶ τὰ δο-
                <lb n="1"/>
              θέντα σημεῖα ἐκτὸς ἔστω τὰ Α Γ, καὶ καθ' ἃ συμβάλλουσιν
                <lb n="2"/>
              τῇ ἐπιφανείᾳ αἱ ἀπὸ τῶν Α Γ ἐπὶ τὸ Β ἐπιζευγνύμεναι
                <lb n="3"/>
              εἰλήφθω σημεῖα τὰ Δ Ε, δι' ὧν γεγράφθω μέγιστος κύκλος
                <lb n="4"/>
              ὁ ΔΕΖΗ· δοθεῖσαι ἄρα αἱ ΑΔ ΓΕ [1λῆμμα γάρ]1· καὶ διὰ
                <lb n="5"/>
              τὸ δεδόσθαι τὴν ἐκ τοῦ κέντρου τῆς σφαίρας καὶ ὅλαι δο-
                <lb n="6"/>
              θήσονται αἱ ΑΒ ΓΒ. </s>
              <s id="id.000225">ἔστιν δὲ καὶ ἡ τὰ δοθέντα ἐπιζευ-
                <lb n="7"/>
              γνύουσα ἡ ΑΓ δοθεῖσα. </s>
              <s id="id.000226">ἐκ τριῶν οὖν τῶν ΑΒ ΑΓ ΓΒ
                <lb n="8"/>
              τρίγωνον συνεστάτω τὸ ΘΚΛ, καὶ περὶ κέντρον τὸ Θ γε-
                <lb n="9"/>
              γράφθω κύκλος ἴσος τῷ ΕΔΖΗ ὁ ΣΜΝΟ. </s>
              <s id="id.000227">ἐὰν μὲν οὗτος
                <lb n="10"/>
              τέμνῃ τὴν ΚΛ, δῆλον ὅτι καὶ ἡ ἐπὶ τὰ Α Γ ἐπιζευγνυμένη
                <lb n="11"/>
              τέμνει τὴν σφαῖραν, εἰ δὲ μή, οὐ τέμνει. </s>
              <s id="id.000228">τεμνέτω οὖν ὁ
                <lb n="12"/>
              κύκλος τὴν ΚΛ κατὰ τὰ Μ Ν, καὶ τῇ μὲν ΣΜ περιφερείᾳ
                <lb n="13"/>
              ἴση ἀπειλήφθω ἡ ΔΗ, τῇ δὲ ΟΝ ἡ ΕΖ. </s>
              <s id="id.000229">φανερὸν δὴ ὅτι
                <lb n="14"/>
              τὰ Η Ζ σημεῖα ἔσται καθ' ἃ τέμνει ἡ ἐπιζευγνύουσα τὰ
                <lb n="15"/>
              Α Γ σημεῖα τὴν τῆς σφαίρας ἐπιφάνειαν.
                <lb n="16"/>
              </s>
            </p>
            <p>
              <s id="id.000230">κγ#. </s>
              <s id="id.000231">Χρήσιμα καὶ τὰ ἐν τοῖς ἰδίως λεγομένοις ὀργανι-
                <lb n="17"/>
              κοῖς καὶ μάλισθ' ὅταν ἐπὶ τὸ εὔκολον ὑπὸ τῆς ἀναλύσεως
                <lb n="18"/>
              χειραγωγούμενα τὴν ἀνάλογον πεῖραν διαφεύγειν δύνηται,
                <lb n="19"/>
              οἷον εἰς τὸν δοθέντα κύκλον ἑπτὰ ἑξάγωνα ἐγγράψαι, τὸ
                <lb n="20"/>
              μὲν περὶ τὸ αὐτὸ κέντρον τῷ κύκλῳ, τὰ δὲ λοιπὰ ἓξ ἀπὸ
                <lb n="21"/>
              μὲν τῶν τοῦ μέσου πλευρῶν ἀναγεγραμμένα, τὰς δὲ ἀντι-
                <lb n="22"/>
              κειμένας πλευρὰς ἔχοντα ἐνηρμοσμένας ἑκάστην εἰς τὴν τοῦ
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              κύκλου περιφέρειαν.
                <lb n="24"/>
              </s>
            </p>
            <p>
              <s id="id.000232">Ἔστω ὁ δοθεὶς κύκλος περὶ κέντρον τὸ Η, καὶ κείσθω
                <lb n="25"/>
              περὶ τὸ αὐτὸ κέντρον ἑξαγώνου πλευρὰ ἡ ΘΚ, ὥστε ἔσται
                <lb n="26"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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