Pappus Alexandrinus, Mathematical Collection, Book 8, 1876

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    <archimedes>
      <text>
        <body>
          <chap>
            <p>
              <s id="id.000105">
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              αὐτῇ πρὸς ὀρθὰς καὶ τῷ ΑΒΓΔ ἐπιπέδῳ ἡ ΜΟ· καὶ ἡ
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              ΟΓ ἄρα πρὸς ὀρθάς ἐστιν τῇ ΡΠ διὰ λῆμμα σφαιρικῶν·
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              ὀρθὴ ἄρα ἐστὶν ἑκατέρα τῶν ὑπὸ ΑΓΠ ΟΓΠ· τὸ ΚΘΛΓ
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              ἄρα ἐπίπεδον κέκλιται πρὸς τὸ [ἀπὸ] ΑΒΓΔ ἐν τῇ δο-
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              θείσῃ γωνίᾳ τῇ ὑπὸ ΕΖΗ.
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              </s>
            </p>
            <p>
              <s id="id.000106">Ἀλλὰ δὴ ἔστω μείζων ἡ ΑΒ τῆς ΑΔ, τῶν ἄλλων
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              ὑποκειμένων τῶν αὐτῶν· λέγω ὅτι ἡ ὑπὸ ΑΓΠ ὀξεῖά
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              ἐστιν.
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              </s>
            </p>
            <p>
              <s id="id.000107">Ἐπεὶ γάρ ἐστιν ὡς μὲν ἡ ΑΠ πρὸς ΠΔ, ἡ ΘΑ πρὸς
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              ΔΛ, ὡς δὲ ἡ ΑΡ πρὸς ΡΒ, ἡ ΘΑ πρὸς ΒΚ, καὶ ἴση
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              ἐστὶν ἡ ΔΛ τῇ ΒΚ, καὶ ὡς ἄρα ἡ ΑΠ πρὸς ΠΔ, ἡ ΑΡ
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              πρὸς ΡΒ· καὶ διελόντι ἄρα ἐστὶν ὡς ἡ ΑΔ πρὸς ΔΠ,
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              οὕτως ἡ ΑΒ πρὸς ΒΡ, καὶ ἐναλλὰξ ὡς ἡ ΑΔ πρὸς ΑΒ,
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              οὕτως ἡ ΔΠ πρὸς ΒΡ. </s>
              <s id="id.000108">ἐλάττων δὲ ἡ ΑΔ τῆς ΑΒ· ἐλάτ-
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              των ἄρα καὶ ἡ ΔΠ τῆς ΒΡ· ὅλη ἄρα ἡ ΑΠ ἐλάττων
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              ἐστὶν τῆς ΑΡ, ὥστε καὶ γωνία ἡ ὑπὸ ΑΡΠ ἐλάσσων ἐστὶν
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              τῆς ὑπὸ ΑΠΡ· μείζων ἄρα ἡ ὑπὸ ΑΠΡ τῆς ὑπὸ ΑΡΠ.
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              </s>
              <s id="id.000109">ἔστιν δὲ καὶ ἡ ὑπὸ ΓΑΠ τῆς ὑπὸ ΓΑΡ μείζων· λοιπὴ
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              ἄρα ἡ ὑπὸ ΑΓΠ τοῦ ΑΓΠ τριγώνου λοιπῆς τῆς ὑπὸ ΑΓΡ
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              τοῦ ΑΓΡ τριγώνου ἐλάσσων ἐστίν· ὀξεῖα ἄρα ἡ ὑπὸ ΑΓΠ
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              γωνία· ἡ κλίσις ἄρα τῶν εἰρημένων ἐπιπέδων πρός τι ση-
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              μεῖον μεταξὺ τῶν Γ Π θεωρεῖται, ἀπὸ τοῦ Α σημείου
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              ἐπὶ τὴν ΓΠ καθέτου ἀγομένης. </s>
              <s id="id.000110">ὡς οὖν ἐκκλῖναι δυνατόν
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              ἐστιν ἐπίπεδον ἐν τῇ δοθείσῃ γωνία πρὸς ἐπίπεδον, δυνα-
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              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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