헬라어 텍스트

헬라어 텍스트

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ἑκάτερον ἄρα τῶν ΖΞ, ΝΛ ἴσον ἐστὶ τῷ ὑπὸ τῶν ΑΗ, ΗΒ.
(유클리드, Elements, book 10, type Prop 3614)
καὶ ἐπεὶ αἱ ΑΗ, ΗΒ δυνάμει εἰσὶν ἀσύμμετροι, ἀσύμμετρον ἄρα ἐστὶ τὸ ἀπὸ τῆσ ΑΗ τῷ ἀπὸ τῆσ ΗΒ.
(유클리드, Elements, book 10, type Prop 3615)
ἀλλὰ τῷ μὲν ἀπὸ τῆσ ΑΗ ἴσον ἐστὶ τὸ ΓΘ, τῷ δὲ ἀπὸ τῆσ ΗΒ ἴσον ἐστὶ τὸ ΚΛ·
(유클리드, Elements, book 10, type Prop 3616)
καὶ ἐπεὶ τῶν ἀπὸ τῶν ΑΗ, ΗΒ μέσον ἀνάλογόν ἐστι τὸ ὑπὸ τῶν ΑΗ, ΗΒ, καί ἐστι τῷ μὲν ἀπὸ τῆσ ΑΗ ἴσον τὸ ΓΘ, τῷ δὲ ἀπὸ τῆσ ΗΒ ἴσον τὸ ΚΛ, τῷ δὲ ὑπὸ τῶν ΑΗ, ΗΒ ἴσον τὸ ΝΛ, καὶ τῶν ἄρα ΓΘ, ΚΛ μέσον ἀνάλογόν ἐστι τὸ ΝΛ·
(유클리드, Elements, book 10, type Prop 3620)
ἴση ἄρα ἡ μὲν ΗΕ τῇ ΕΘ, ἡ δὲ ΑΗ τῇ ΒΘ.
(유클리드, Elements, book 11, type Prop40)
καὶ ἐπεὶ πάλιν ἐδείχθη ἡ ΑΗ τῇ ΒΘ ἴση, ἀλλὰ μὴν καὶ ἡ ΖΑ τῇ ΖΒ ἴση, δύο δὴ αἱ ΖΑ, ΑΗ δυσὶ ταῖσ ΖΒ, ΒΘ ἴσαι εἰσίν.
(유클리드, Elements, book 11, type Prop46)
καὶ ἐπεὶ ἴσαι εἰσὶν αἱ ΛΚ, ΚΑ, ΑΕ εὐθεῖαι ἀλλήλαισ, ἴσα ἐστὶ καὶ τὰ μὲν ΛΟ, ΚΦ, ΑΖ παραλληλόγραμμα ἀλλήλοισ, τὰ δὲ ΚΞ, ΚΒ, ΑΗ ἀλλήλοισ καὶ ἔτι τὰ ΛΨ, ΚΠ, ΑΡ ἀλλήλοισ·
(유클리드, Elements, book 11, type Prop455)
Ἔστω ἐπὶ τῆσ αὐτῆσ βάσεωσ τῆσ ΑΒ στερεὰ παραλληλεπίπεδα τὰ ΓΜ, ΓΝ ὑπὸ τὸ αὐτὸ ὕψοσ, ὧν αἱ ἐφεστῶσαι αἱ ΑΗ, ΑΖ, ΛΜ, ΛΝ, ΓΔ, ΓΕ, ΒΘ, ΒΚ ἐπὶ τῶν αὐτῶν εὐθειῶν ἔστωσαν τῶν ΖΝ, ΔΚ·
(유클리드, Elements, book 11, type Prop520)
Ἔστω ἐπὶ τῆσ αὐτῆσ βάσεωσ τῆσ ΑΒ στερεὰ παραλληλεπίπεδα τὰ ΓΜ, ΓΝ ὑπὸ τὸ αὐτὸ ὕψοσ, ὧν αἱ ἐφεστῶσαι αἱ ΑΖ, ΑΗ, ΛΜ, ΛΝ, ΓΔ, ΓΕ, ΒΘ, ΒΚ μὴ ἔστωσαν ἐπὶ τῶν αὐτῶν εὐθειῶν·
(유클리드, Elements, book 11, type Prop536)
ἐπί τε γὰρ πάλιν τῆσ αὐτῆσ βάσεώσ εἰσι τῆσ ΑΓΒΛ καὶ ὑπὸ τὸ αὐτὸ ὕψοσ, ὧν αἱ ἐφεστῶσαι αἱ ΑΗ, ΑΞ, ΓΕ, ΓΠ, ΛΝ, ΛΟ, ΒΚ, ΒΡ ἐπὶ τῶν αὐτῶν εἰσιν εὐθειῶν τῶν ΗΠ, ΝΡ.
(유클리드, Elements, book 11, type Prop542)
Ἔστωσαν δὴ πρότερον αἱ ἐφεστηκυῖαι αἱ ΘΚ, ΒΕ, ΑΗ, ΛΜ, ΟΠ, ΔΖ, ΓΞ, ΡΣ πρὸσ ὀρθὰσ ταῖσ ΑΒ, ΓΔ βάσεσιν, καὶ ἐκβεβλήσθω ἐπ’ εὐθείασ τῇ ΓΡ εὐθεῖα ἡ ΡΤ, καὶ συνεστάτω πρὸσ τῇ ΡΤ εὐθείᾳ καὶ τῷ πρὸσ αὐτῇ σημείῳ τῷ Ρ τῇ ὑπὸ ΑΛΒ γωνίᾳ ἴση ἡ ὑπὸ ΤΡΥ, καὶ κείσθω τῇ μὲν ΑΛ ἴση ἡ ΡΤ, τῇ δὲ ΛΒ ἴση ἡ ΡΥ, καὶ συμπεπληρώσθω ἥ τε ΡΧ βάσισ καὶ τὸ ΨΥ στερεόν.
(유클리드, Elements, book 11, type Prop549)
Μὴ ἔστωσαν δὴ αἱ ἐφεστηκυῖαι αἱ ΑΗ, ΘΚ, ΒΕ, ΛΜ, ΓΝ, ΟΠ, ΔΖ, ΡΣ πρὸσ ὀρθὰσ ταῖσ ΑΒ, ΓΔ βάσεσιν·
(유클리드, Elements, book 11, type Prop574)
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)
καὶ ὡσ ἄρα τὸ ΑΗ παραλληλόγραμμον πρὸσ τὸ ΗΚ, οὕτωσ τὸ ΗΚ πρὸσ τὸ ΚΛ καὶ τὸ ΠΕ πρὸσ τὸ ΚΜ.
(유클리드, Elements, book 11, type Prop607)
ἀλλ’ ὡσ μὲν τὸ ΑΗ πρὸσ τὸ ΗΚ, οὕτωσ τὸ ΑΒ στερεὸν πρὸσ τὸ ΕΞ στερεόν, ὡσ δὲ τὸ ΗΚ πρὸσ τὸ ΚΛ, οὕτωσ τὸ ΞΕ στερεὸν πρὸσ τὸ ΠΛ στερεόν, ὡσ δὲ τὸ ΠΕ πρὸσ τὸ ΚΜ, οὕτωσ τὸ ΠΛ στερεὸν πρὸσ τὸ ΚΟ στερεόν·
(유클리드, Elements, book 11, type Prop608)

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