헬라어 텍스트

헬라어 텍스트

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αἱ ΒΑ, ΑΖ ἄρα ῥηταί εἰσι δυνάμει μόνον σύμμετροι.
(유클리드, Elements, book 10, type Prop 1650)
καὶ ἐπεί [ἐστιν] ὡσ ὁ ΔΓ πρὸσ τὸν ΓΕ, οὕτωσ τὸ ἀπὸ τῆσ ΒΑ πρὸσ τὸ ἀπὸ τῆσ ΑΖ, ἀναστρέψαντι ἄρα ὡσ ὁ ΓΔ πρὸσ τὸν ΔΕ, οὕτωσ τὸ ἀπὸ τῆσ ΑΒ πρὸσ τὸ ἀπὸ τῆσ ΒΖ.
(유클리드, Elements, book 10, type Prop 1651)
Εὑρ́ηνται ἄρα δύο ῥηταὶ δυνάμει μόνον σύμμετροι αἱ ΒΑ, ΑΖ, ὥστε τὴν μείζονα τὴν ΑΒ τῆσ ἐλάσσονοσ τῆσ ΑΖ μεῖζον δύνασθαι τῷ ἀπὸ τῆσ ΒΖ συμμέτρου ἑαυτῇ μήκει·
(유클리드, Elements, book 10, type Prop 1657)
Ἐκκείσθω ῥητὴ ἡ ΑΒ καὶ δύο τετράγωνοι ἀριθμοὶ οἱ ΓΕ, ΕΔ, ὥστε τὸν συγκείμενον ἐξ αὐτῶν τὸν ΓΔ μὴ εἶναι τετράγωνον, καὶ γεγράφθω ἐπὶ τῆσ ΑΒ ἡμικύκλιον τὸ ΑΖΒ, καὶ πεποιήσθω ὡσ ὁ ΔΓ πρὸσ τὸν ΓΕ, οὕτωσ τὸ ἀπὸ τῆσ ΒΑ πρὸσ τὸ ἀπὸ τῆσ ΑΖ, καὶ ἐπεζεύχθω ἡ ΖΒ.
(유클리드, Elements, book 10, type Prop 1660)
Ὁμοίωσ δὴ δείξομεν τῷ πρὸ τούτου, ὅτι αἱ ΒΑ, ΑΖ ῥηταί εἰσι δυνάμει μόνον σύμμετροι.
(유클리드, Elements, book 10, type Prop 1661)
καὶ ἐπεί ἐστιν ὡσ ὁ ΔΓ πρὸσ τὸν ΓΕ, οὕτωσ τὸ ἀπὸ τῆσ ΒΑ πρὸσ τὸ ἀπὸ τῆσ ΑΖ, ἀναστρέψαντι ἄρα ὡσ ὁ ΓΔ πρὸσ τὸν ΔΕ, οὕτωσ τὸ ἀπὸ τῆσ ΑΒ πρὸσ τὸ ἀπὸ τῆσ ΒΖ.
(유클리드, Elements, book 10, type Prop 1662)
λέγω, ὅτι τὸ μὲν ὑπὸ τῶν ΓΒΔ ἴσον ἐστὶ τῷ ἀπὸ τῆσ ΒΑ, τὸ δὲ ὑπὸ τῶν ΒΓΔ ἴσον τῷ ἀπὸ τῆσ ΓΑ, καὶ τὸ ὑπὸ τῶν ΒΔ, ΔΓ ἴσον τῷ ἀπὸ τῆσ ΑΔ, καὶ ἔτι τὸ ὑπὸ τῶν ΒΓ, ΑΔ ἴσον [ἐστὶ] τῷ ὑπὸ τῶν ΒΑ, ΑΓ.
(유클리드, Elements, book 10, type Prop 1706)
Καὶ πρῶτον, ὅτι τὸ ὑπὸ τῶν ΓΒΔ ἴσον [ἐστὶ] τῷ ἀπὸ τῆσ ΒΑ.
(유클리드, Elements, book 10, type Prop 1707)
καὶ ἐπεὶ ὅμοιόν ἐστι τὸ ΑΒΓ τρίγωνον τῷ ΑΒΔ τριγώνῳ, ἔστιν ἄρα ὡσ ἡ ΓΒ πρὸσ τὴν ΒΑ, οὕτωσ ἡ ΒΑ πρὸσ τὴν ΒΔ·
(유클리드, Elements, book 10, type Prop 1709)
Λέγω, ὅτι καὶ τὸ ὑπὸ τῶν ΒΓ, ΑΔ ἴσον ἐστὶ τῷ ὑπὸ τῶν ΒΑ, ΑΓ.
(유클리드, Elements, book 10, type Prop 1714)
ἐπεὶ γάρ, ὡσ ἔφαμεν, ὅμοιόν ἐστι τὸ ΑΒΓ τῷ ΑΒΔ, ἔστιν ἄρα ὡσ ἡ ΒΓ πρὸσ τὴν ΓΑ, οὕτωσ ἡ ΒΑ πρὸσ τὴν ΑΔ.
(유클리드, Elements, book 10, type Prop 1715)
] τὸ ἄρα ὑπὸ τῶν ΒΓ, ΑΔ ἴσον ἐστὶ τῷ ὑπὸ τῶν ΒΑ, ΑΓ·
(유클리드, Elements, book 10, type Prop 1717)
καί ἐστιν ὡσ ἡ ΑΕ πρὸσ ΕΒ, οὕτωσ τὸ ὑπὸ τῶν ΒΑ, ΑΕ πρὸσ τὸ ὑπὸ τῶν ΑΒ, ΒΕ, ἴσον δὲ τὸ μὲν ὑπὸ τῶν ΒΑ, ΑΕ τῷ ἀπὸ τῆσ ΑΖ, τὸ δὲ ὑπὸ τῶν ΑΒ, ΒΕ τῷ ἀπὸ τῆσ ΒΖ·
(유클리드, Elements, book 10, type Prop 1722)
Ἐπεὶ ἀσύμμετρόσ ἐστιν ἡ ΑΖ τῇ ΖΒ, ἀσύμμετρον ἄρα ἐστὶ καὶ τὸ ὑπὸ τῶν ΒΑ, ΑΖ τῷ ὑπὸ τῶν ΑΒ, ΒΖ.
(유클리드, Elements, book 10, type Prop 1741)
ἴσον δὲ τὸ μὲν ὑπὸ τῶν ΒΑ, ΑΖ τῷ ἀπὸ τῆσ ΑΔ, τὸ δὲ ὑπὸ τῶν ΑΒ, ΒΖ τῷ ἀπὸ τῆσ ΔΒ·
(유클리드, Elements, book 10, type Prop 1742)

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