헬라어 텍스트

헬라어 텍스트

헬라어 문장 내 검색 Language

Ὁσαπλάσιον γάρ ἐστι τὸ ΑΕ τοῦ ΓΖ, τοσαυταπλάσιον γεγονέτω καὶ τὸ ΕΒ τοῦ ΓΗ.
(유클리드, Elements, book 5, type Prop48)
ἔστω πρότερον τὸ ΑΕ ἔλαττον τοῦ ΕΒ, καὶ πεπολλαπλασιάσθω τὸ ΑΕ, καὶ ἔστω αὐτοῦ πολλαπλάσιον τὸ ΖΗ μεῖζον ὂν τοῦ Δ, καὶ ὁσαπλάσιόν ἐστι τὸ ΖΗ τοῦ ΑΕ, τοσαυταπλάσιον γεγονέτω καὶ τὸ μὲν ΗΘ τοῦ ΕΒ τὸ δὲ Κ τοῦ Γ·
(유클리드, Elements, book 5, type Prop103)
καὶ ὁσαπλάσιόν ἐστι τὸ ΗΘ τοῦ ΕΒ, τοσαυταπλάσιον γεγονέτω καὶ τὸ μὲν ΖΗ τοῦ ΑΕ, τὸ δὲ Κ τοῦ Γ.
(유클리드, Elements, book 5, type Prop130)
καὶ συμπεπληρώσθω τὸ ΔΗ παραλληλόγραμμον, καὶ ἐκκείσθω τισ εὐθεῖα ἡ Κ, καὶ γεγονέτω ὡσ μὲν ἡ ΒΓ πρὸσ τὴν ΓΗ, οὕτωσ ἡ Κ πρὸσ τὴν Λ, ὡσ δὲ ἡ ΔΓ πρὸσ τὴν ΓΕ, οὕτωσ ἡ Λ πρὸσ τὴν Μ.
(유클리드, Elements, book 6, type Prop473)
εἰ γὰρ δυνατόν, προσευρήσθω ὁ Δ, ὥστε εἶναι ὡσ τὸν Α πρὸσ τὸν Β, τὸν Γ πρὸσ τὸν Δ, καὶ γεγονέτω ὡσ ὁ Β πρὸσ τὸν Γ, ὁ Δ πρὸσ τὸν Ε.
(유클리드, Elements, book 9, type Prop394)
γεγονέτω, καὶ λελείφθω τὸ ΑΗ ἔλασσον τοῦ Ε.
(유클리드, Elements, book 10, type Prop 121)
Ἐκκείσθωσαν γὰρ δύο ἀριθμοὶ οἱ Β, Γ πρὸσ ἀλλήλουσ λόγον μὴ ἔχοντεσ, ὃν τετράγωνοσ ἀριθμὸσ πρὸσ τετράγωνον ἀριθμόν, τουτέστι μὴ ὅμοιοι ἐπίπεδοι, καὶ γεγονέτω ὡσ ὁ Β πρὸσ τὸν Γ, οὕτωσ τὸ ἀπὸ τῆσ Α τετράγωνον πρὸσ τὸ ἀπὸ τῆσ Δ τετράγωνον·
(유클리드, Elements, book 10, type Prop 1210)
Ἐκκείσθωσαν δύο ῥηταὶ δυνάμει μόνον σύμμετροι αἱ Α, Β, καὶ εἰλήφθω τῶν Α, Β μέση ἀνάλογον ἡ Γ, καὶ γεγονέτω ὡσ ἡ Α πρὸσ τὴν Β, οὕτωσ ἡ Γ πρὸσ τὴν Δ.
(유클리드, Elements, book 10, type Prop 1569)
Ἐκκείσθωσαν [τρεῖσ] ῥηταὶ δυνάμει μόνον σύμμετροι αἱ Α, Β, Γ, καὶ εἰλήφθω τῶν Α, Β μέση ἀνάλογον ἡ Δ, καὶ γεγονέτω ὡσ ἡ Β πρὸσ τὴν Γ, ἡ Δ πρὸσ τὴν Ε.
(유클리드, Elements, book 10, type Prop 1586)
Ἐκκείσθωσαν δύο μέσαι δυνάμει μόνον σύμμετροι αἱ ΑΒ, ΒΓ μέσον περιέχουσαι, ὥστε τὴν ΑΒ τῆσ ΒΓ μεῖζον δύνασθαι τῷ ἀπὸ ἀσυμμέτρου ἑαυτῇ, καὶ γεγράφθω ἐπὶ τῆσ ΑΒ ἡμικύκλιον τὸ ΑΔΒ, καὶ τὰ λοιπὰ γεγονέτω τοῖσ ἐπάνω ὁμοίωσ.
(유클리드, Elements, book 10, type Prop 1753)
καὶ γεγονέτω ὡσ ὁ ΒΑ ἀριθμὸσ πρὸσ τὸν ΑΓ, οὕτωσ τὸ ἀπὸ τῆσ ΕΖ πρὸσ τὸ ἀπὸ τῆσ ΖΗ.
(유클리드, Elements, book 10, type Prop 24)
γεγονέτω δὴ καὶ ὡσ ὁ ΓΑ ἀριθμὸσ πρὸσ τὸν ΑΒ, οὕτωσ τὸ ἀπὸ τῆσ ΕΖ πρὸσ τὸ ἀπὸ τῆσ ΖΗ·
(유클리드, Elements, book 10, type Prop 228)
καὶ ἐκκείσθω τισ ῥητὴ εὐθεῖα ἡ Ε, καὶ γεγονέτω ὡσ ὁ Δ πρὸσ τὸν ΑΒ, οὕτωσ τὸ ἀπὸ τῆσ Ε πρὸσ τὸ ἀπὸ τῆσ ΖΗ·
(유클리드, Elements, book 10, type Prop 249)
γεγονέτω δὴ πάλιν ὡσ ὁ ΒΑ ἀριθμὸσ πρὸσ τὸν ΑΓ, οὕτωσ τὸ ἀπὸ τῆσ ΖΗ πρὸσ τὸ ἀπὸ τῆσ ΗΘ·
(유클리드, Elements, book 10, type Prop 255)
καὶ γεγονέτω ὡσ ὁ ΒΑ ἀριθμὸσ πρὸσ τὸν ΑΓ, οὕτωσ τὸ ἀπὸ τῆσ ΕΖ πρὸσ τὸ ἀπὸ τῆσ ΖΗ·
(유클리드, Elements, book 10, type Prop 282)

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