# Synagoge 3.14

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.14

14 ί. Τρίγωνον τὸ ΑBΓ ἔχον ἑκάστην τῶν πλευρῶν δοθεῖσαν, καὶ σημεῖον ἐντὸς τὸ ∠, καὶ ὧ ὑπερέχει ἡ Α∠ τῆς Γ∠, τούτῳ ὑπερεχέτω καὶ ἡ Γ∠ τῆς ∠Β, καὶ ἔστω ὑπεροχὴ δοθεῖσα· ὅτι ἑκάστη τῶν Α∠ ∠Γ ∠Β δοθεῖσά ἐστιν. Ἐπεὶ ἡ τῶν Α∠ ∠Γ ὑπεροχή δοθεῖσά ἐστιν , ἔστω τῇ ὑπεροχῇ ἴση ἑκατέρα τῶν ΑΕ ΒΖ· αἱ τρεῖς ἄρα αἱ Ε∠ ∠Γ ∠Ζ ἴσαι ἀλλήλαις εἰσίν. γεγράφθω περὶ κέντρον τὸ ∠ κύκλος ὁ ΓΕΖ· διὰ δὴ τὸ προγεγραμμένον δοθεῖσά ἐστιν ἡ ∠Ζ. ἧς ἡ ΒΖ ἐστὶν δοθεῖσα ἡ λοιπὴ ἄρα ἡ Β∠ ἐστὶν δοθεῖσα. ἀλλὰ καὶ ἑκατέρα τῶν Α∠ ∠Γ δοθεῖσά ἐστιν· ἑκάστη ἄρα τῶν Α∠ ∠Γ ∠Β ἐστὶν δοθεῖσα.

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Pappus Alexandrinus, Synagoge, ed. Friedrich Hultsch. Text: The Greek Library, from the Perseus Digital Library and other open sources, CC BY-SA 4.0. Changes: apostrophes normalised and the text divided into reading sections by Interlinea.
License: CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/). Source: https://thegreeklibrary.pages.lisn.upsaclay.fr/works/tlg2032.tlg001.local001/.