헬라어 텍스트

헬라어 텍스트

헬라어 문장 내 검색 Language

ἐπεὶ ἰσάκισ ἐστὶ πολλαπλάσιον τὸ ΑΗ τοῦ Ε καὶ τὸ ΓΘ τοῦ Ζ, ἴσον δὲ τὸ μὲν ΗΒ τῷ Ε, τὸ δὲ ΚΓ τῷ Ζ, ἰσάκισ ἄρα ἐστὶ πολλαπλάσιον τὸ ΑΒ τοῦ Ε καὶ τὸ ΚΘ τοῦ Ζ.
(유클리드, Elements, book 5, type Prop67)
διῃρήσθω τὸ μὲν ΑΒ εἰσ τὰ τῷ Γ ἴσα τὰ ΑΗ, ΗΘ, ΘΒ, τὸ δὲ ΔΕ εἰσ τὰ τῷ Ζ ἴσα τὰ ΔΚ, ΚΛ, ΛΕ·
(유클리드, Elements, book 5, type Prop239)
ἔσται δὴ ἴσον τὸ πλῆθοσ τῶν ΑΗ, ΗΘ, ΘΒ τῷ πλήθει τῶν ΔΚ, ΚΛ, ΛΕ.
(유클리드, Elements, book 5, type Prop240)
καὶ ἐπεὶ ἴσα ἐστὶ τὰ ΑΗ, ΗΘ, ΘΒ ἀλλήλοισ, ἔστι δὲ καὶ τὰ ΔΚ, ΚΛ, ΛΕ ἴσα ἀλλήλοισ, ἔστιν ἄρα ὡσ τὸ ΑΗ πρὸσ τὸ ΔΚ, οὕτωσ τὸ ΗΘ πρὸσ τὸ ΚΛ, καὶ τὸ ΘΒ πρὸσ τὸ ΛΕ.
(유클리드, Elements, book 5, type Prop241)
ἔστιν ἄρα ὡσ τὸ ΑΗ πρὸσ τὸ ΔΚ, οὕτωσ τὸ ΑΒ πρὸσ τὸ ΔΕ.
(유클리드, Elements, book 5, type Prop243)
ἴσον δὲ τὸ μὲν ΑΗ τῷ Γ, τὸ δὲ ΔΚ τῷ Ζ·
(유클리드, Elements, book 5, type Prop244)
λέγω, ὅτι καὶ συντεθὲν πρῶτον καὶ πέμπτον τὸ ΑΗ πρὸσ δεύτερον τὸ Γ τὸν αὐτὸν ἕξει λόγον, καὶ τρίτον καὶ ἕκτον τὸ ΔΘ πρὸσ τέταρτον τὸ Ζ.
(유클리드, Elements, book 5, type Prop376)
ἔστιν ἄρα ὡσ τὸ ΑΗ πρὸσ τὸ ΗΒ, οὕτωσ τὸ ΔΘ πρὸσ τὸ ΘΕ.
(유클리드, Elements, book 5, type Prop380)
δι’ ἴσου ἄρα ἐστὶν ὡσ τὸ ΑΗ πρὸσ τὸ Γ, οὕτωσ τὸ ΔΘ πρὸσ τὸ Ζ.
(유클리드, Elements, book 5, type Prop382)
Κείσθω γὰρ τῷ μὲν Ε ἴσον τὸ ΑΗ, τῷ δὲ Ζ ἴσον τὸ ΓΘ.
(유클리드, Elements, book 5, type Prop388)
Ἐπεὶ [οὖν] ἐστιν ὡσ τὸ ΑΒ πρὸσ τὸ ΓΔ, οὕτωσ τὸ Ε πρὸσ τὸ Ζ, ἴσον δὲ τὸ μὲν Ε τῷ ΑΗ, τὸ δὲ Ζ τῷ ΓΘ, ἔστιν ἄρα ὡσ τὸ ΑΒ πρὸσ τὸ ΓΔ, οὕτωσ τὸ ΑΗ πρὸσ τὸ ΓΘ.
(유클리드, Elements, book 5, type Prop389)
καὶ ἐπεί ἐστιν ὡσ ὅλον τὸ ΑΒ πρὸσ ὅλον τὸ ΓΔ, οὕτωσ ἀφαιρεθὲν τὸ ΑΗ πρὸσ ἀφαιρεθὲν τὸ ΓΘ, καὶ λοιπὸν ἄρα τὸ ΗΒ πρὸσ λοιπὸν τὸ ΘΔ ἔσται ὡσ ὅλον τὸ ΑΒ πρὸσ ὅλον τὸ ΓΔ.
(유클리드, Elements, book 5, type Prop390)
καὶ ἐπεὶ ἴσον ἐστὶ τὸ μὲν ΑΗ τῷ Ε, τὸ δὲ ΓΘ τῷ Ζ, τὰ ἄρα ΑΗ, Ζ ἴσα ἐστὶ τοῖσ ΓΘ, Ε.
(유클리드, Elements, book 5, type Prop393)
Καὶ [ἐπεὶ] ἐὰν [ἀνίσοισ ἴσα προστεθῇ, τὰ ὅλα ἄνισά ἐστιν, ἐὰν ἄρα] τῶν ΗΒ, ΘΔ ἀνίσων ὄντων καὶ μείζονοσ τοῦ ΗΒ τῷ μὲν ΗΒ προστεθῇ τὰ ΑΗ, Ζ, τῷ δὲ ΘΔ προστεθῇ τὰ ΓΘ, Ε, συνάγεται τὰ ΑΒ, Ζ μείζονα τῶν ΓΔ, Ε.
(유클리드, Elements, book 5, type Prop394)
Ἐκβεβλήσθω γὰρ ἡ ΒΔ ἐφ’ ἑκάτερα τὰ μέρη ἐπὶ τὰ Θ, Λ σημεῖα, καὶ κείσθωσαν τῇ μὲν ΒΓ βάσει ἴσαι [ὁσαιδηποτοῦν] αἱ ΒΗ, ΗΘ, τῇ δὲ ΓΔ βάσει ἴσαι ὁσαιδηποτοῦν αἱ ΔΚ, ΚΛ, καὶ ἐπεζεύχθωσαν αἱ ΑΗ, ΑΘ, ΑΚ, ΑΛ.
(유클리드, Elements, book 6, type Prop4)

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