Pappus Alexandrinus, Mathematical Collection, Book 8, 1876

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              <s id="id.000173">
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              Θ Ν]1. </s>
              <s id="id.000174">καὶ ἐπεὶ ὡς τὸ ὑπὸ ΞΔΛ πρὸς τὸ ὑπὸ τῶν ΜΔΚ,
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              οὕτως τὸ ὑπὸ ΞΓΛ πρὸς ἑκάτερον τῶν ὑπὸ ΗΓΠ ΝΓΘ,
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              ἔσται ἄρα ἴσον τὸ ὑπὸ ΗΓΠ τῷ ὑπὸ ΝΓΘ. </s>
              <s id="id.000175">καὶ ἔστιν
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              δοθὲν τὸ ὑπὸ ΝΓΘ [1δοθεῖσα γὰρ ἑκατέρα]1· δοθὲν ἄρα τὸ
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              Π. </s>
              <s id="id.000176">ἀλλὰ καὶ τὸ Κ· θέσει ἄρα ἡ ΚΠΞ. </s>
              <s id="id.000177">ἀλλὰ καὶ ἡ ΛΓΞ·
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              δοθὲν ἄρα τὸ Ξ. </s>
              <s id="id.000178">καὶ ἔστιν ἐπὶ τῆς ἐλλείψεως. </s>
              <s id="id.000179">ἐπιζευχ-
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              θεῖσαι δὴ αἱ ΝΞ ΛΘ συμπιπτέτωσαν τῇ ΕΖ διαμέτρῳ
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              ἐκβληθείσῃ κατὰ τὰ Ρ Σ· ἔσται δὴ πάλιν ὡς τὸ ὑπὸ ΝΓΘ
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              πρὸς τὸ ὑπὸ ΞΓΛ, οὕτως τὸ ὑπὸ ΝΑΘ πρὸς ἑκάτερον
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              τῶν ὑπὸ ΡΑΣ ΕΑΖ, καὶ διὰ τοῦτο ἴσον τὸ ὑπὸ ΡΑΣ τῷ
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              ὑπὸ ΕΑΖ. </s>
              <s id="id.000180">καὶ ἔστιν δοθὲν τὸ ὑπὸ ΡΑΣ [1δοθεῖσαι γάρ
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              εἰσιν αἱ ΡΑ ΑΣ]1· δοθὲν ἄρα καὶ τὸ ὑπὸ ΕΑ ΑΖ. </s>
              <s id="id.000181">τῷ
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              δ' ὁμοίῳ τρόπῳ δειχθήσεται καὶ τὸ ὑπὸ ΕΒΖ δοθέν. </s>
              <s id="id.000182">καὶ
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              δοθέντα τὰ Α Β· δοθέντα ἄρα καὶ τὰ Ε Ζ, ὡς ἑξῆς δειχ-
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              θήσεται· ὥστε ἡ ΕΖ διάμετρος δέδοται τῷ μεγέθει. </s>
              <s id="id.000183">δῆλον
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              δ' ὅτι καὶ ἡ συζυγὴς αὐτῇ· δέδοται γὰρ ὁ τῆς ΕΖ πλαγίας
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              </s>
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