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Ἐκκείσθω
τισ εὐθεῖα ἡ ΔΕ πεπερασμένη μὲν κατὰ τὸ Δ ἄπειροσ δὲ κατὰ τὸ Ε, καὶ κείσθω τῇ μὲν Α ἴση ἡ ΔΖ, τῇ δὲ Β ἴση ἡ ΖΗ, τῇ δὲ Γ ἴση ἡ ΗΘ·
(유클리드, Elements, book 1, type Prop282)
Ἐκκείσθω
τισ εὐθεῖα ἡ ΑΒ, καὶ τετμήσθω κατὰ τὸ Γ σημεῖον, ὥστε τὸ ὑπὸ τῶν ΑΒ, ΒΓ περιεχόμενον ὀρθογώνιον ἴσον εἶναι τῷ ἀπὸ τῆσ ΓΑ τετραγώνῳ·
(유클리드, Elements, book 4, type Prop160)
Ἐκκείσθω
τρίγωνον ἰσοσκελὲσ τὸ ΖΗΘ διπλασίονα ἔχον ἑκατέραν τῶν πρὸσ τοῖσ Η, Θ γωνιῶν τῆσ πρὸσ τῷ Ζ, καὶ ἐγγεγράφθω εἰσ τὸν ΑΒΓΔΕ κύκλον τῷ ΖΗΘ τριγώνῳ ἰσογώνιον τρίγωνον τὸ ΑΓΔ, ὥστε τῇ μὲν πρὸσ τῷ Ζ γωνίᾳ ἴσην εἶναι τὴν ὑπὸ ΓΑΔ, ἑκατέραν δὲ τῶν πρὸσ τοῖσ Η, Θ ἴσην ἑκατέρᾳ τῶν ὑπὸ ΑΓΔ, ΓΔΑ·
(유클리드, Elements, book 4, type Prop187)
καὶ συμπεπληρώσθω τὸ ΔΗ παραλληλόγραμμον, καὶ
ἐκκείσθω
τισ εὐθεῖα ἡ Κ, καὶ γεγονέτω ὡσ μὲν ἡ ΒΓ πρὸσ τὴν ΓΗ, οὕτωσ ἡ Κ πρὸσ τὴν Λ, ὡσ δὲ ἡ ΔΓ πρὸσ τὴν ΓΕ, οὕτωσ ἡ Λ πρὸσ τὴν Μ.
(유클리드, Elements, book 6, type Prop473)
Ἔστωσαν δύο ἀριθμοὶ πρῶτοι πρὸσ ἀλλήλουσ οἱ Α, Β καὶ εἰσ αὐτοὺσ μεταξὺ κατὰ τὸ συνεχὲσ ἀνάλογον ἐμπιπτέτωσαν οἱ Γ, Δ, καὶ
ἐκκείσθω
ἡ Ε μονάσ·
(유클리드, Elements, book 8, type Prop160)
ἐκκείσθω
γὰρ μονάσ.
(유클리드, Elements, book 9, type Prop564)
Ἐκκείσθω
γὰρ ῥητὴ ἡ ΓΔ, καὶ τῷ μὲν ἀπὸ τῆσ Α ἴσον παρὰ τὴν ΓΔ παραβεβλήσθω χωρίον ὀρθογώνιον τὸ ΓΕ πλάτοσ ποιοῦν τὴν ΕΔ·
(유클리드, Elements, book 10, type Prop 1477)
καὶ
ἐκκείσθω
ῥητὴ ἡ ΖΗ, καὶ τῷ μὲν ΑΔ ἴσον παρὰ τὴν ΖΗ παραβεβλήσθω ὀρθογώνιον παραλληλόγραμμον τὸ ΗΘ πλάτοσ ποιοῦν τὴν ΖΘ, τῷ δὲ ΑΓ ἴσον παρὰ τὴν ΘΜ παραβεβλήσθω ὀρθογώνιον παραλληλόγραμμον τὸ ΜΚ πλάτοσ ποιοῦν τὴν ΘΚ, καὶ ἔτι τῷ ΒΕ ἴσον ὁμοίωσ παρὰ τὴν ΚΝ παραβεβλήσθω τὸ ΝΛ πλάτοσ ποιοῦν τὴν ΚΛ·
(유클리드, Elements, book 10, type Prop 1512)
Εἰ γὰρ δυνατόν, μέσον τὸ ΑΒ μέσου τοῦ ΑΓ ὑπερεχέτω ῥητῷ τῷ ΔΒ, καὶ
ἐκκείσθω
ῥητὴ ἡ ΕΖ, καὶ τῷ ΑΒ ἴσον παρὰ τὴν ΕΖ παραβεβλήσθω παραλληλόγραμμον ὀρθογώνιον τὸ ΖΘ πλάτοσ ποιοῦν τὴν ΕΘ, τῷ δὲ ΑΓ ἴσον ἀφῃρήσθω τὸ ΖΗ·
(유클리드, Elements, book 10, type Prop 1541)
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)
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)
Ἐκκείσθω
γὰρ ῥητὴ ἡ ΔΕ, καὶ τῷ ἀπὸ τῆσ ΑΓ ἴσον παρὰ τὴν ΔΕ παραβεβλήσθω τὸ ΔΖ πλάτοσ ποιοῦν τὴν ΔΗ.
(유클리드, Elements, book 10, type Prop 1796)
Ἐκκείσθω
ῥητὴ ἡ ΔΕ, καὶ παραβεβλήσθω παρὰ τὴν ΔΕ τοῖσ μὲν ἀπὸ τῶν ΑΒ, ΒΓ ἴσον τὸ ΔΖ, τῷ δὲ δὶσ ὑπὸ τῶν ΑΒ, ΒΓ ἴσον τὸ ΗΘ·
(유클리드, Elements, book 10, type Prop 1841)
Ἐκκείσθω
εὐθεῖα ἡ ΑΒ καὶ τετμήσθω ἡ ὅλη εἰσ ἄνισα καθ’ ἑκάτερον τῶν Γ, Δ, ὑποκείσθω δὲ μείζων ἡ ΑΓ τῆσ ΔΒ·
(유클리드, Elements, book 10, type Prop 1858)
καὶ
ἐκκείσθω
ῥητὴ ἡ ΕΖ, καὶ τῷ μὲν ἀπὸ τῆσ ΑΒ ἴσον παρὰ τὴν ΕΖ παραλληλόγραμμον ὀρθογώνιον παραβεβλήσθω τὸ ΕΚ, τοῖσ δὲ ἀπὸ τῶν ΑΓ, ΓΒ ἴσον ἀφῃρήσθω τὸ ΕΗ·
(유클리드, Elements, book 10, type Prop 1911)
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