# Synagoge 3.12

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.12

Ἄλλως. 12 η΄· Ἤχθω κάθετος ἐπὶ τὴν ΑΓ ἡ ΜΕ καὶ ἐκβεβλήοθω ἐπὶ τὸ Ζ. ἐπεὶ δοθεῖσά ἐστιν ἑκάστη τῶν Α∠ ∠Γ· ΓΑ, καὶ κάθετος ἡ ∠Ε, δοθεῖσα ἔσται καὶ ἑκατέρα τῶν ΑΕ ΕΓ, καὶ ἐπεὶ ἰσογώνιόν ἐστιν τὸ ΑΒΓ τρίγωνον τῷ ΓΕΖ τριγώνῳ, ἔστιν ὡς ἡ ΓΕ πρὸς EΖ, ἡ ΓΒ πρὸς ΒΑ. δοθεὶς δὲ ὁ τῆς ΓΒ πρὸς ΒΑ λόγος: δοθεὶς ἄρα καὶ ὁ ΓΕ πρὸς ΕΖ λόγος. καὶ δοθεῖσά ἐστιν ἡ ΓΕ· δοθεῖσα ἄρα καὶ ἡ ΕΖ. ἦν δὲ καὶ ἡ ∠Ε δοθεῖσα καὶ ὅλη ἄρα ἡ ∠Ζ ἔσται δοθεῖσα. κατά ταὐτὰ δοθήσεται καὶ ἑκατέρα τῶν ΒΖ ΖΓ· ὡς γὰρ ἡ ΑΓ πρὸς ΒΓ, οὕτως ἡ ΖΓ πρὸς ΓΕ. καὶ δοθεὶς ὁ τῆς ΑΓ πρὸς ΓΒ λόγος). ἤχθω δὴ πάλιν ἀπὸ τοῦ ∠ κάθετος ἡ ∠Η· δοθεῖσα ἄρα ἑκατέρα τῶν ΖΗ ΗΓ, ὣστε καὶ ἑκατέρα τῶν ΒΗ Η∠ δοθεῖσά ἐστι. καὶ ὀρθή ἐστιν ἡ Η γωνία δοθεῖσα ἅρα ἐστὶν καὶ ἡ Β∠.

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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/.