헬라어 텍스트

헬라어 텍스트

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εἰ δὲ ἡ ΑΕ [τῆσ ΕΒ] μεῖζον δύναται τῷ ἀπὸ ἀσυμμέτρου ἑαυτῇ, καὶ ἡ ΓΖ τῆσ ΖΔ μεῖζον δυνήσεται τῷ ἀπὸ ἀσυμμέτρου ἑαυτῇ.
(유클리드, Elements, book 10, type Prop 3644)
καὶ εἰ μὲν σύμμετρόσ ἐστιν ἡ ΑΕ τῇ ἐκκειμένῃ ῥητῇ μήκει, καὶ ἡ ΓΖ, εἰ δὲ ἡ ΒΕ, καὶ ἡ ΔΖ, εἰ δὲ οὐδετέρα τῶν ΑΕ, ΕΒ, οὐδετέρα τῶν ΓΖ, ΖΔ.
(유클리드, Elements, book 10, type Prop 3645)
αἱ ΑΕ, ΕΒ ἄρα μέσαι εἰσὶ δυνάμει μόνον σύμμετροι.
(유클리드, Elements, book 10, type Prop 3652)
σύμμετροσ ἄρα [ἐστὶ] καὶ ἡ ΑΕ τῇ ΓΖ, ἡ δὲ ΒΕ τῇ ΔΖ.
(유클리드, Elements, book 10, type Prop 3654)
αἱ δὲ ΑΕ, ΕΒ μέσαι εἰσὶ δυνάμει μόνον σύμμετροι·
(유클리드, Elements, book 10, type Prop 3655)
Ἐπεὶ [γάρ] ἐστιν ὡσ ἡ ΑΕ πρὸσ τὴν ΕΒ, οὕτωσ ἡ ΓΖ πρὸσ τὴν ΖΔ [ἀλλ’ ὡσ μὲν ἡ ΑΕ πρὸσ τὴν ΕΒ, οὕτωσ τὸ ἀπὸ τῆσ ΑΕ πρὸσ τὸ ὑπὸ τῶν ΑΕ, ΕΒ, ὡσ δὲ ἡ ΓΖ πρὸσ τὴν ΖΔ, οὕτωσ τὸ ἀπὸ τῆσ ΓΖ πρὸσ τὸ ὑπὸ τῶν ΓΖ, ΖΔ], ἔστιν ἄρα καὶ ὡσ τὸ ἀπὸ τῆσ ΑΕ πρὸσ τὸ ὑπὸ τῶν ΑΕ, ΕΒ, οὕτωσ τὸ ἀπὸ τῆσ ΓΖ πρὸσ τὸ ὑπὸ τῶν ΓΖ, ΖΔ [καὶ ἐναλλὰξ ὡσ τὸ ἀπὸ τῆσ ΑΕ πρὸσ τὸ ἀπὸ τῆσ ΓΖ, οὕτωσ τὸ ὑπὸ τῶν ΑΕ, ΕΒ πρὸσ τὸ ὑπὸ τῶν ΓΖ, ΖΔ].
(유클리드, Elements, book 10, type Prop 3659)
σύμμετρον δὲ τὸ ἀπὸ τῆσ ΑΕ τῷ ἀπὸ τῆσ ΓΖ·
(유클리드, Elements, book 10, type Prop 3660)
σύμμετρον ἄρα ἐστὶ καὶ τὸ ὑπὸ τῶν ΑΕ, ΕΒ τῷ ὑπὸ τῶν ΓΖ, ΖΔ.
(유클리드, Elements, book 10, type Prop 3661)
εἴτε οὖν ῥητόν ἐστι τὸ ὑπὸ τῶν ΑΕ, ΕΒ, ῥητὸν ἔσται καὶ τὸ ὑπὸ τῶν ΓΖ, ΖΔ, εἴτε μέσον [ἐστὶ] τὸ ὑπὸ τῶν ΑΕ, ΕΒ, μέσον [ἐστὶ] καὶ τὸ ὑπὸ τῶν ΓΖ, ΖΔ.
(유클리드, Elements, book 10, type Prop 3662)
καὶ ἐπεὶ αἱ ΑΕ, ΕΒ δυνάμει εἰσὶν ἀσύμμετροι, καὶ αἱ ΓΖ, ΖΔ ἄρα δυνάμει εἰσὶν ἀσύμμετροι.
(유클리드, Elements, book 10, type Prop 3669)
ἐπεὶ οὖν ἐστιν ὡσ ἡ ΑΕ πρὸσ τὴν ΕΒ, οὕτωσ ἡ ΓΖ πρὸσ τὴν ΖΔ, ἔστιν ἄρα καὶ ὡσ τὸ ἀπὸ τῆσ ΑΕ πρὸσ τὸ ἀπὸ τῆσ ΕΒ, οὕτωσ τὸ ἀπὸ τῆσ ΓΖ πρὸσ τὸ ἀπὸ τῆσ ΖΔ.
(유클리드, Elements, book 10, type Prop 3670)
συνθέντι ἄρα ἐστὶν ὡσ τὰ ἀπὸ τῶν ΑΕ, ΕΒ πρὸσ τὸ ἀπὸ τῆσ ΕΒ, οὕτωσ τὰ ἀπὸ τῶν ΓΖ, ΖΔ πρὸσ τὸ ἀπὸ τῆσ ΖΔ [καὶ ἐναλλάξ]·
(유클리드, Elements, book 10, type Prop 3671)
σύμμετρον ἄρα καὶ τὸ συγκείμενον ἐκ τῶν ἀπὸ τῶν ΑΕ, ΕΒ τετραγώνων τῷ συγκειμένῳ ἐκ τῶν ἀπὸ τῶν ΓΖ, ΖΔ τετραγώνων.
(유클리드, Elements, book 10, type Prop 3673)
ῥητὸν δέ ἐστι τὸ συγκείμενον ἐκ τῶν ἀπὸ τῶν ΑΕ, ΕΒ τετραγώνων·
(유클리드, Elements, book 10, type Prop 3674)
πάλιν, ἐπεί ἐστιν ὡσ τὸ ἀπὸ τῆσ ΑΕ πρὸσ τὸ ὑπὸ τῶν ΑΕ, ΕΒ, οὕτωσ τὸ ἀπὸ τῆσ ΓΖ πρὸσ τὸ ὑπὸ τῶν ΓΖ, ΖΔ, σύμμετρον δὲ τὸ ἀπὸ τῆσ ΑΕ τετράγωνον τῷ ἀπὸ τῆσ ΓΖ τετραγώνῳ, σύμμετρον ἄρα ἐστὶ καὶ τὸ ὑπὸ τῶν ΑΕ, ΕΒ τῷ ὑπὸ τῶν ΓΖ, ΖΔ.
(유클리드, Elements, book 10, type Prop 3676)

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