헬라어 텍스트

헬라어 텍스트

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ὃ δὲ μέροσ ἐστὶν ὁ ΑΕ τοῦ ΓΖ, τὸ αὐτὸ μέροσ ὑπόκειται καὶ ὁ ΑΒ τοῦ ΓΔ·
(유클리드, Elements, book 7, type Prop151)
καὶ ἐπεί, ὃ μέροσ ἐστὶν ὁ ΑΕ τοῦ ΓΖ, τὸ αὐτὸ μέροσ [ἐστὶ] καὶ ὁ ΕΒ τοῦ ΗΓ, ἴσοσ δὲ ὁ ΗΓ τῷ ΖΔ, ὃ ἄρα μέροσ ἐστὶν ὁ ΑΕ τοῦ ΓΖ, τὸ αὐτὸ μέροσ ἐστὶ καὶ ὁ ΕΒ τοῦ ΖΔ.
(유클리드, Elements, book 7, type Prop156)
ἀλλὰ ὃ μέροσ ἐστὶν ὁ ΑΕ τοῦ ΓΖ, τὸ αὐτὸ μέροσ ἐστὶ καὶ ὁ ΑΒ τοῦ ΓΔ·
(유클리드, Elements, book 7, type Prop157)
Ἀριθμὸσ γὰρ ὁ ΑΒ ἀριθμοῦ τοῦ ΓΔ μέρη ἔστω, ἅπερ ἀφαιρεθεὶσ ὁ ΑΕ ἀφαιρεθέντοσ τοῦ ΓΖ·
(유클리드, Elements, book 7, type Prop161)
ἃ ἄρα μέρη ἐστὶν ὁ ΗΘ τοῦ ΓΔ, τὰ αὐτὰ μέρη ἐστὶ καὶ ὁ ΑΕ τοῦ ΓΖ.
(유클리드, Elements, book 7, type Prop164)
διῃρήσθω ὁ μὲν ΗΘ εἰσ τὰ τοῦ ΓΔ μέρη τὰ ΗΚ, ΚΘ, ὁ δὲ ΑΕ εἰσ τὰ τοῦ ΓΖ μέρη τὰ ΑΛ, ΛΕ·
(유클리드, Elements, book 7, type Prop165)
Ἔστω ὡσ ὅλοσ ὁ ΑΒ πρὸσ ὅλον τὸν ΓΔ, οὕτωσ ἀφαιρεθεὶσ ὁ ΑΕ πρὸσ ἀφαιρεθέντα τὸν ΓΖ·
(유클리드, Elements, book 7, type Prop204)
Ἐπεί ἐστιν ὡσ ὁ ΑΒ πρὸσ τὸν ΓΔ, οὕτωσ ὁ ΑΕ πρὸσ τὸν ΓΖ, ὃ ἄρα μέροσ ἐστὶν ὁ ΑΒ τοῦ ΓΔ ἢ μέρη, τὸ αὐτὸ μέροσ ἐστὶ καὶ ὁ ΑΕ τοῦ ΓΖ ἢ τὰ αὐτὰ μέρη.
(유클리드, Elements, book 7, type Prop206)
λέγω, ὅτι ὅλοσ ὁ ΑΕ ἄρτιόσ ἐστιν.
(유클리드, Elements, book 9, type Prop451)
ὥστε καὶ ὅλοσ ὁ ΑΕ ἔχει μέροσ ἥμισυ.
(유클리드, Elements, book 9, type Prop453)
ἄρτιοσ ἄρα ἐστὶν ὁ ΑΕ·
(유클리드, Elements, book 9, type Prop455)
λέγω, ὅτι ὅλοσ ὁ ΑΕ ἄρτιόσ ἐστιν.
(유클리드, Elements, book 9, type Prop459)
καὶ ὅλοσ ἄρα ὁ ΑΕ ἄρτιόσ ἐστιν·
(유클리드, Elements, book 9, type Prop463)
καὶ ὅλοσ ἄρα ὁ ΑΕ ἄρτιόσ ἐστιν.
(유클리드, Elements, book 9, type Prop471)
Καὶ ἐπεὶ [δύο] εὐθεῖαι ἄνισοί εἰσιν αἱ ΑΒ, ΒΓ, καὶ ἡ ΑΒ τῆσ ΒΓ μεῖζον δύναται τῷ ἀπὸ ἀσυμμέτρου ἑαυτῇ, τῷ δὲ τετάρτῳ τοῦ ἀπὸ τῆσ ΒΓ, τουτέστι τῷ ἀπὸ τῆσ ἡμισείασ αὐτῆσ, ἴσον παρὰ τὴν ΑΒ παραβέβληται παραλληλόγραμμον ἐλλεῖπον εἴδει τετραγώνῳ καὶ ποιεῖ τὸ ὑπὸ τῶν ΑΕΒ, ἀσύμμετροσ ἄρα ἐστὶν ἡ ΑΕ τῇ ΕΒ.
(유클리드, Elements, book 10, type Prop 1721)

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