헬라어 텍스트

헬라어 텍스트

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καὶ ἐπεί, ὃ μέροσ ἐστὶν ὁ ΑΗ τοῦ Γ, τὸ αὐτὸ μέροσ ἐστὶ καὶ ὁ ΔΘ τοῦ Ζ, ὃ ἄρα μέροσ ἐστὶν ὁ ΑΗ τοῦ Γ, τὸ αὐτὸ μέροσ ἐστὶ καὶ συναμφότεροσ ὁ ΑΗ, ΔΘ συναμφοτέρου τοῦ Γ, Ζ.
(유클리드, Elements, book 7, type Prop142)
διῃρήσθω ὁ μὲν ΑΒ εἰσ τὰ τοῦ Γ μέρη τὰ ΑΗ, ΗΒ, ὁ δὲ ΔΕ εἰσ τὰ τοῦ Ζ μέρη τὰ ΔΘ, ΘΕ·
(유클리드, Elements, book 7, type Prop195)
ἔσται δὴ ἴσον τὸ πλῆθοσ τῶν ΑΗ, ΗΒ τῷ πλήθει τῶν ΔΘ, ΘΕ.
(유클리드, Elements, book 7, type Prop196)
καὶ ἐπεί, ὃ μέροσ ἐστὶν ὁ ΑΗ τοῦ Γ, τὸ αὐτὸ μέροσ ἐστὶ καὶ ὁ ΔΘ τοῦ Ζ, καὶ ἐναλλάξ, ὃ μέροσ ἐστὶν ὁ ΑΗ τοῦ ΔΘ ἢ μέρη, τὸ αὐτὸ μέροσ ἐστὶ καὶ ὁ Γ τοῦ Ζ ἢ τὰ αὐτὰ μέρη.
(유클리드, Elements, book 7, type Prop197)
ὥστε καί [ὃ μέροσ ἐστὶν ὁ ΑΗ τοῦ ΔΘ ἢ μέρη, τὸ αὐτὸ μέροσ ἐστὶ καὶ ὁ ΗΒ τοῦ ΘΕ ἢ τὰ αὐτὰ μέρη·
(유클리드, Elements, book 7, type Prop199)
καὶ ὃ ἄρα μέροσ ἐστὶν ὁ ΑΗ τοῦ ΔΘ ἢ μέρη, τὸ αὐτὸ μέροσ ἐστὶ καὶ ὁ ΑΒ τοῦ ΔΕ ἢ τὰ αὐτὰ μέρη·
(유클리드, Elements, book 7, type Prop200)
ἀλλ’ ὃ μέροσ ἐστὶν ὁ ΑΗ τοῦ ΔΘ ἢ μέρη, τὸ αὐτὸ μέροσ ἐδείχθη καὶ ὁ Γ τοῦ Ζ ἢ τὰ αὐτὰ μέρη, καὶ] ἃ [ἄρα] μέρη ἐστὶν ὁ ΑΒ τοῦ ΔΕ ἢ μέροσ, τὰ αὐτὰ μέρη ἐστὶ καὶ ὁ Γ τοῦ Ζ ἢ τὸ αὐτὸ μέροσ·
(유클리드, Elements, book 7, type Prop201)
καὶ τὸ μὲν ΑΒ τὸ ΖΔ καταμετροῦν λειπέτω ἑαυτοῦ ἔλασσον τὸ ΓΖ, τὸ δὲ ΓΖ τὸ ΒΗ καταμετροῦν λειπέτω ἑαυτοῦ ἔλασσον τὸ ΑΗ, καὶ τοῦτο ἀεὶ γινέσθω, ἑώσ οὗ λειφθῇ τι μέγεθοσ, ὅ ἐστιν ἔλασσον τοῦ Ε.
(유클리드, Elements, book 10, type Prop 120)
γεγονέτω, καὶ λελείφθω τὸ ΑΗ ἔλασσον τοῦ Ε.
(유클리드, Elements, book 10, type Prop 121)
καὶ λοιπὸν ἄρα τὸ ΑΗ μετρήσει, τὸ μεῖζον τὸ ἔλασσον.
(유클리드, Elements, book 10, type Prop 128)
ἐπεὶ οὖν ὅλοσ ὁ ΑΓ ὅλου τοῦ ΓΔ ἐστι διπλασίων, ὧν ὁ ΑΗ τοῦ ΔΕ ἐστι διπλασίων, καὶ λοιπὸσ ἄρα ὁ ΗΓ λοιποῦ τοῦ ΕΓ ἐστι διπλασίων·
(유클리드, Elements, book 10, type Prop 1621)
παραβεβλήσθω οὖν παρὰ τὴν ΑΕ τῷ ἀπὸ τῆσ ΕΖ ἴσον τὸ ὑπὸ ΑΗ, ΗΕ·
(유클리드, Elements, book 10, type Prop 2179)
σύμμετροσ ἄρα ἐστὶν ἡ ΑΗ τῇ ΕΗ μήκει.
(유클리드, Elements, book 10, type Prop 2180)
καὶ ἐπεὶ τὸ ὑπὸ τῶν ΑΗ, ΗΕ ἴσον ἐστὶ τῷ ἀπὸ τῆσ ΕΖ, ἔστιν ἄρα ὡσ ἡ ΑΗ πρὸσ ΕΖ, οὕτωσ ἡ ΖΕ πρὸσ ΕΗ·
(유클리드, Elements, book 10, type Prop 2186)
Ἐπεὶ γὰρ σύμμετρόσ ἐστιν ἡ ΑΗ τῇ ΗΕ, σύμμετρόσ ἐστι καὶ ἡ ΑΕ ἑκατέρᾳ τῶν ΑΗ, ΗΕ.
(유클리드, Elements, book 10, type Prop 2198)

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