헬라어 텍스트

헬라어 텍스트

헬라어 문장 내 검색 Language

ἴσον ἄρα καὶ τὸ ἀπὸ τῆσ ΒΓ εἶδοσ τοῖσ ἀπὸ τῶν ΒΑ, ΑΓ εἴδεσι τοῖσ ὁμοίοισ τε καὶ ὁμοίωσ ἀναγραφομένοισ.
(유클리드, Elements, book 6, type Prop634)
Ἔστω δύο τρίγωνα τὰ ΑΒΓ, ΔΓΕ τὰσ δύο πλευρὰσ τὰσ ΒΑ, ΑΓ ταῖσ δυσὶ πλευραῖσ ταῖσ ΔΓ, ΔΕ ἀνάλογον ἔχοντα, ὡσ μὲν τὴν ΑΒ πρὸσ τὴν ΑΓ, οὕτωσ τὴν ΔΓ πρὸσ τὴν ΔΕ, παράλληλον δὲ τὴν μὲν ΑΒ τῇ ΔΓ, τὴν δὲ ΑΓ τῇ ΔΕ·
(유클리드, Elements, book 6, type Prop638)
καὶ ἐπεὶ δύο τρίγωνά ἐστι τὰ ΑΒΓ, ΔΓΕ μίαν γωνίαν τὴν πρὸσ τῷ Α μιᾷ γωνίᾳ τῇ πρὸσ τῷ Δ ἴσην ἔχοντα, περὶ δὲ τὰσ ἴσασ γωνίασ τὰσ πλευρὰσ ἀνάλογον, ὡσ τὴν ΒΑ πρὸσ τὴν ΑΓ, οὕτωσ τὴν ΓΔ πρὸσ τὴν ΔΕ, ἰσογώνιον ἄρα ἐστὶ τὸ ΑΒΓ τρίγωνον τῷ ΔΓΕ τριγώνῳ·
(유클리드, Elements, book 6, type Prop643)
μετρεῖ δὲ καὶ ὅλον τὸν ΒΑ·
(유클리드, Elements, book 7, type Prop8)
καὶ ὅλον ἄρα τὸν ΒΑ μετρήσει·
(유클리드, Elements, book 7, type Prop40)
μετρεῖ δὲ καὶ ὅλον τὸν ΒΑ·
(유클리드, Elements, book 7, type Prop48)
ἴσοσ δὲ συναμφότεροσ μὲν ὁ ΜΚ, ΝΘ τῷ ΕΒ, ὁ δὲ ΘΗ τῷ ΒΑ·
(유클리드, Elements, book 7, type Prop177)
μετρεῖ δὲ καὶ τὸν ΒΑ·
(유클리드, Elements, book 7, type Prop422)
λέγω, ὅτι ῥητή ἐστιν ἡ ΒΓ καὶ σύμμετροσ τῇ ΒΑ μήκει.
(유클리드, Elements, book 10, type Prop 1412)
ἴση δὲ ἡ ΔΒ τῇ ΒΑ·
(유클리드, Elements, book 10, type Prop 1419)
καὶ ἐπεὶ ἴση ἐστὶν ἡ μὲν ΔΒ τῇ ΒΑ, ἡ δὲ ΞΒ τῇ ΒΓ, ἔστιν ἄρα ὡσ ἡ ΔΒ πρὸσ τὴν ΒΓ, οὕτωσ ἡ ΑΒ πρὸσ τὴν ΒΞ.
(유클리드, Elements, book 10, type Prop 1522)
Ἐκκείσθω γάρ τισ ῥητὴ ἡ ΑΒ καὶ δύο τετράγωνοι ἀριθμοὶ οἱ ΓΔ, ΔΕ, ὥστε τὴν ὑπεροχὴν αὐτῶν τὸν ΓΕ μὴ εἶναι τετράγωνον, καὶ γεγράφθω ἐπὶ τῆσ ΑΒ ἡμικύκλιον τὸ ΑΖΒ, καὶ πεποιήσθω ὡσ ὁ ΔΓ πρὸσ τὸν ΓΕ, οὕτωσ τὸ ἀπὸ τῆσ ΒΑ τετράγωνον πρὸσ τὸ ἀπὸ τῆσ ΑΖ τετράγωνον καὶ ἐπεζεύχθω ἡ ΖΒ.
(유클리드, Elements, book 10, type Prop 1642)
Ἐπεὶ [οὖν] ἐστιν ὡσ τὸ ἀπὸ τῆσ ΒΑ πρὸσ τὸ ἀπὸ τῆσ ΑΖ, οὕτωσ ὁ ΔΓ πρὸσ τὸν ΓΕ, τὸ ἀπὸ τῆσ ΒΑ ἄρα πρὸσ τὸ ἀπὸ τῆσ ΑΖ λόγον ἔχει, ὃν ἀριθμὸσ ὁ ΔΓ πρὸσ ἀριθμὸν τὸν ΓΕ·
(유클리드, Elements, book 10, type Prop 1643)
σύμμετρον ἄρα ἐστὶ τὸ ἀπὸ τῆσ ΒΑ τῷ ἀπὸ τῆσ ΑΖ.
(유클리드, Elements, book 10, type Prop 1644)
καὶ ἐπεὶ ὁ ΔΓ πρὸσ τὸν ΓΕ λόγον οὐκ ἔχει, ὃν τετράγωνοσ ἀριθμὸσ πρὸσ τετράγωνον ἀριθμόν, οὐδὲ τὸ ἀπὸ τῆσ ΒΑ ἄρα πρὸσ τὸ ἀπὸ τῆσ ΑΖ λόγον ἔχει, ὃν τετράγωνοσ ἀριθμὸσ πρὸσ τετράγωνον ἀριθμόν·
(유클리드, Elements, book 10, type Prop 1648)

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