Ancient Greek · ~2 min
19. Ad prop. XCΙ. Ἄλλως.
Euclid, Data (demonstrationes alterae) 19. Ad prop. XCΙ. Ἄλλως.
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Εἰλήφθω τὸ κέντρον τοῦ κύκλου τὸ Ε, καὶ ἐπε- ζεύχθω ἡ ΔΕ καὶ διήχθω ἐπὶ τὸ Α. καὶ ἐπεὶ δοθέν ἐστιν ἑκάτερον τῶν Ε, Δ, δοθεῖσα ἄρα ἐστὶν ἡ ΕΔ· θέσει δὲ καὶ ὁ ΑΒΖ κύκλος· δοθὲν ἄρα ἐστὶν ἑκάτε- ρον τῶν Α, Ζ. ἔστι δὲ καὶ τὸ Δ δοθέν· δοθεῖσα ἄρα ἐστὶν ἑκατέρα τῶν ΑΔ, ΔΖ· δοθὲν ἄρα ἐστὶ τὸ ὑπὸ τῶν ΑΔΖ· καί ἐστιν ἴσον τῷ ὑπὸ τῶν ΒΔ, ΔΓ· δοθὲν ἄρα ἐστὶ καὶ τὸ ὑπὸ τῶν ΒΔ, ΔΓ.