헬라어 텍스트

헬라어 텍스트

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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)
καὶ ἐπεὶ ὁ ΒΑ πρὸσ τὸν ΑΓ λόγον οὐκ ἔχει, ὃν τετράγωνοσ ἀριθμὸσ πρὸσ τετράγωνον ἀριθμόν, οὐδὲ τὸ ἀπὸ τῆσ ΕΖ ἄρα πρὸσ τὸ ἀπὸ τῆσ ΖΗ λόγον ἔχει, ὃν τετράγωνοσ ἀριθμὸσ πρὸσ τετράγωνον ἀριθμόν·
(유클리드, Elements, book 10, type Prop 210)
Ἐπεὶ γάρ ἐστιν ὡσ ὁ ΒΑ ἀριθμὸσ πρὸσ τὸν ΑΓ, οὕτωσ τὸ ἀπὸ τῆσ ΕΖ πρὸσ τὸ ἀπὸ τῆσ ΖΗ, μείζων δὲ ὁ ΒΑ τοῦ ΑΓ, μεῖζον ἄρα καὶ τὸ ἀπὸ τῆσ ΕΖ τοῦ ἀπὸ τῆσ ΖΗ.
(유클리드, Elements, book 10, type Prop 215)
καὶ ἐπεί ἐστιν ὡσ ὁ ΒΑ πρὸσ τὸν ΑΓ, οὕτωσ τὸ ἀπὸ τῆσ ΕΖ πρὸσ τὸ ἀπὸ τῆσ ΖΗ, ἀναστρέψαντι ἄρα ἐστὶν ὡσ ὁ ΑΒ πρὸσ τὸν ΒΓ, οὕτωσ τὸ ἀπὸ τῆσ ΕΖ πρὸσ τὸ ἀπὸ τῆσ Θ.
(유클리드, Elements, book 10, type Prop 217)
Ἐπεὶ γὰρ ἀνάπαλίν ἐστιν ὡσ ὁ ΒΑ ἀριθμὸσ πρὸσ τὸν ΑΓ, οὕτωσ τὸ ἀπὸ τῆσ ΗΖ πρὸσ τὸ ἀπὸ τῆσ ΖΕ, μείζων δὲ ὁ ΒΑ τοῦ ΑΓ, μεῖζον ἄρα [καὶ] τὸ ἀπὸ τῆσ ΗΖ τοῦ ἀπὸ τῆσ ΖΕ.
(유클리드, Elements, book 10, type Prop 236)
ἐκκείσθω δέ τισ καὶ ἄλλοσ μὴ τετράγωνοσ ἀριθμὸσ ὁ Δ, καὶ πρὸσ ἑκάτερον τῶν ΒΑ, ΑΓ λόγον μὴ ἐχέτω, ὃν τετράγωνοσ ἀριθμὸσ πρὸσ τετράγωνον ἀριθμόν·
(유클리드, Elements, book 10, type Prop 248)
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 ἐπεὶ ὁ ΒΑ πρὸσ τὸν ΑΓ λόγον οὐκ ἔχει, ὅν τετράγωνοσ ἀριθμὸσ πρὸσ τετράγωνον ἀριθμόν, οὐδὲ τὸ ἀπὸ τῆσ ΖΗ πρὸσ τὸ ἀπὸ τῆσ ΘΗ λόγον ἔχει, ὃν τετράγωνοσ ἀριθμὸσ πρὸσ τετράγωνον ἀριθμόν·
(유클리드, Elements, book 10, type Prop 259)
Ἐπεὶ γάρ ἐστιν ὡσ ὁ Δ πρὸσ τὸν ΑΒ, οὕτωσ τὸ ἀπὸ τῆσ Ε πρὸσ τὸ ἀπὸ τῆσ ΖΗ, ὡσ δὲ ὁ ΒΑ πρὸσ τὸν ΑΓ, οὕτωσ τὸ ἀπὸ τῆσ ΖΗ πρὸσ τὸ ἀπὸ τῆσ ΗΘ, δι’ ἴσου ἄρα ἐστὶν ὡσ ὁ Δ πρὸσ τὸν ΑΓ, οὕτωσ τὸ ἀπὸ τῆσ Ε πρὸσ τὸ ἀπὸ τῆσ ΗΘ.
(유클리드, Elements, book 10, type Prop 264)
καὶ ἐπεί ἐστιν ὡσ ὁ ΒΑ πρὸσ τὸν ΑΓ, οὕτωσ τὸ ἀπὸ τῆσ ΖΗ πρὸσ τὸ ἀπὸ τῆσ ΗΘ, μεῖζον ἄρα τὸ ἀπὸ τῆσ ΖΗ τοῦ ἀπὸ τῆσ ΗΘ.
(유클리드, Elements, book 10, type Prop 268)
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)
καὶ ἐπεὶ ὁ ΒΑ πρὸσ τὸν ΑΓ λόγον οὐκ ἔχει, ὃν τετράγωνοσ ἀριθμὸσ πρὸσ τετράγωνον ἀριθμόν, οὐδὲ τὸ ἀπὸ τῆσ ΕΖ πρὸσ τὸ ἀπὸ τῆσ ΖΗ λόγον ἔχει, ὃν τετράγωνοσ ἀριθμὸσ πρὸσ τετράγωνον ἀριθμόν·
(유클리드, Elements, book 10, type Prop 285)
Ἐπεὶ γάρ ἐστιν ὡσ ὁ ΒΑ πρὸσ τὸν ΑΓ, οὕτωσ τὸ ἀπὸ τῆσ ΕΖ πρὸσ τὸ ἀπὸ τῆσ ΖΗ [μείζων δὲ ὁ ΒΑ τοῦ ΑΓ], μεῖζον ἄρα τὸ ἀπὸ τῆσ ΕΖ τοῦ ἀπὸ τῆσ ΖΗ.
(유클리드, Elements, book 10, type Prop 290)
Ἐπεὶ γάρ ἐστιν ὡσ ὁ ΓΑ πρὸσ τὸν ΑΒ, οὕτωσ τὸ ἀπὸ τῆσ ΕΖ πρὸσ τὸ ἀπὸ τῆσ ΖΗ, ἀνάπαλιν ὡσ ὁ ΒΑ πρὸσ τὸν ΑΓ, οὕτωσ τὸ ἀπὸ τῆσ ΖΗ πρὸσ τὸ ἀπὸ τῆσ ΖΕ·
(유클리드, Elements, book 10, type Prop 2109)
ἔστω δὲ καὶ ἕτεροσ ἀριθμὸσ ὁ Δ μὴ τετράγωνοσ ὢν μηδὲ πρὸσ ἑκάτερον τῶν ΒΑ, ΑΓ λόγον ἔχων, ὃν τετράγωνοσ ἀριθμὸσ πρὸσ τετράγωνον ἀριθμόν·
(유클리드, Elements, book 10, type Prop 2122)

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