헬라어 텍스트

헬라어 텍스트

헬라어 문장 내 검색 Language

καὶ ἐπεὶ διὰ τὴν ὁμοιότητα τῶν ΑΒ, ΓΔ στερεῶν ἐστιν ὡσ ἡ ΑΕ πρὸσ τὴν ΓΖ, οὕτωσ ἡ ΕΗ πρὸσ τὴν ΖΝ, καὶ ἡ ΕΘ πρὸσ τὴν ΖΡ, ἴση δὲ ἡ μέν ΓΖ τῇ ΕΚ, ἡ δὲ ΖΝ τῇ ΕΛ, ἡ δὲ ΖΡ τῇ ΕΜ, ἔστιν ἄρα ὡσ ἡ ΑΕ πρὸσ τὴν ΕΚ, οὕτωσ ἡ ΗΕ πρὸσ τὴν ΕΛ καὶ ἡ ΘΕ πρὸσ τὴν ΕΜ.
(유클리드, Elements, book 11, type Prop605)
ἀλλ’ ὡσ μὲν ἡ ΑΕ πρὸσ τὴν ΕΚ, οὕτωσ τὸ ΑΗ [παραλληλόγραμμον] πρὸσ τὸ ΗΚ παραλληλόγραμμον, ὡσ δὲ ἡ ΗΕ πρὸσ τὴν ΕΛ, οὕτωσ τὸ ΗΚ πρὸσ τὸ ΚΛ, ὡσ δὲ ἡ ΘΕ πρὸσ ΕΜ, οὕτωσ τὸ ΠΕ πρὸσ τὸ ΚΜ·
(유클리드, Elements, book 11, type Prop606)
ἀλλ’ ὡσ τὸ ΑΒ πρὸσ τὸ ΕΞ, οὕτωσ τὸ ΑΗ παραλληλόγραμμον πρὸσ τὸ ΗΚ καὶ ἡ ΑΕ εὐθεῖα πρὸσ τὴν ΕΚ·
(유클리드, Elements, book 11, type Prop612)
ὥστε καὶ τὸ ΑΒ στερεὸν πρὸσ τὸ ΚΟ τριπλασίονα λόγον ἔχει ἤπερ ἡ ΑΕ πρὸσ τὴν ΕΚ.
(유클리드, Elements, book 11, type Prop613)
καὶ τὸ ΑΒ ἄρα στερεὸν πρὸσ τὸ ΓΔ στερεὸν τριπλασίονα λόγον ἔχει ἤπερ ἡ ὁμόλογοσ αὐτοῦ πλευρὰ ἡ ΑΕ πρὸσ τὴν ὁμόλογον πλευρὰν τὴν ΓΖ.
(유클리드, Elements, book 11, type Prop615)
καὶ ἐπεὶ ὅμοιον τὸ ΑΒΓΔΕ πολύγωνον τῷ ΖΗΘΚΛ πολυγώνῳ, ἴση ἐστὶ καὶ ἡ ὑπὸ ΒΑΕ γωνία τῇ ὑπὸ ΗΖΛ, καί ἐστιν ὡσ ἡ ΒΑ πρὸσ τὴν ΑΕ, οὕτωσ ἡ ΗΖ πρὸσ τὴν ΖΛ.
(유클리드, Elements, book 12, type Prop5)
ἐπεὶ ἴση ἐστὶν ἡ μὲν ΑΕ τῇ ΕΒ, ἡ δὲ ΑΘ τῇ ΔΘ, παράλληλοσ ἄρα ἐστὶν ἡ ΕΘ τῇ ΔΒ.
(유클리드, Elements, book 12, type Prop72)
καὶ ἡ ΑΕ ἄρα τῇ ΘΚ ἐστιν ἴση.
(유클리드, Elements, book 12, type Prop77)
τετμήσθωσαν αἱ ΑΒ, ΒΓ, ΓΔ, ΔΑ περιφέρειαι δίχα κατὰ τὰ Ε, Ζ, Η, Θ σημεῖα, καὶ ἐπεζεύχθωσαν αἱ ΑΕ, ΕΒ, ΒΖ, ΖΓ, ΓΗ, ΗΔ, ΔΘ, ΘΑ·
(유클리드, Elements, book 12, type Prop267)
λελείφθω, καὶ ἔστω τὰ ΑΕ, ΕΒ, ΒΖ, ΖΓ, ΓΗ, ΗΔ, ΔΘ, ΘΑ·
(유클리드, Elements, book 12, type Prop274)
τετμήσθωσαν αἱ ΑΒ, ΒΓ, ΓΔ, ΔΑ περιφέρειαι δίχα κατὰ τὰ Ε, Ζ, Η, Θ σημεῖα, καὶ ἐπεζεύχθωσαν αἱ ΑΕ, ΕΒ, ΒΖ, ΖΓ, ΓΗ, ΗΔ, ΔΘ, ΘΑ·
(유클리드, Elements, book 12, type Prop296)
λελείφθω, καὶ ἔστω τὰ ἐπὶ τῶν ΑΕ, ΕΒ, ΒΖ, ΖΓ, ΓΗ, ΗΔ, ΔΘ, ΘΑ·
(유클리드, Elements, book 12, type Prop301)
Ἀναγεγράφθωσαν γὰρ ἀπὸ τῶν ΑΒ, ΔΓ τετράγωνα τὰ ΑΕ, ΔΖ, καὶ καταγεγράφθω ἐν τῷ ΔΖ τὸ σχῆμα, καὶ διήχθω ἡ ΖΓ ἐπὶ τὸ Η.
(유클리드, Elements, book 13, type Prop4)
ὅλον ἄρα τὸ ΑΕ τετράγωνον ἴσον ἐστὶ τῷ ΜΝΞ γνώμονι.
(유클리드, Elements, book 13, type Prop14)
καὶ ἐπεὶ διπλῆ ἐστιν ἡ ΒΑ τῆσ ΑΔ, τετραπλάσιόν ἐστι τὸ ἀπὸ τῆσ ΒΑ τοῦ ἀπὸ τῆσ ΑΔ, τουτέστι τὸ ΑΕ τοῦ ΔΘ.
(유클리드, Elements, book 13, type Prop15)

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