# Synagoge 3.70

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.70

70 Ἔστω γὰρ κύκλου τοῦ ΚΛΘ περιφέρενει ἡ ΛΘ, καὶ δέον ἔστω τεμεῖν αὐτὴν εἰς δοθέντα λόγον. Ἐπὶ τὸ κέντρον αἱ ΛΒΘ, καὶ τῇ ΒΘ πρὸς ὀρθὰς ἡ ΒΚ, καὶ διὰ τοῦ Κ γεγράφθω τετραγωνίζουσα γραμμὴ ἡ ΚΑ∠Γ, καὶ κάθετος ἀχθεῖσα ἡ ΑΕ τετμήσθω κατὰ τὸ Ζ, ὥστε εἶναι ὡς τὴν ΑΖ πρὸς ΖΕ, οὕτως τὸν δοθέντα λόγον εἰς ὃν διελεῖν θέλομεν τὴν γωνίαν, καὶ τῇ μὲν ΒΓ παράλληλος ἡ Ζ∠, ἐπεζεύχθω δὲ ἡ Β∠, καὶ κάθετος ἡ ∠Η. ἐπεὶ οὖν διὰ τὸ σύμπτωμα τῆς γραμμῆς ἐστιν ὡς ἡ ΑΕ πρὸς ∠Η, τουτέστιν πρὸς ΖΕ, ἡ ὑπὸ ΑΒΓ γωνία πρὸς τὴν ὑπὸ ∠ΒΓ, διελόντι ἄρα ἐστὶν ὡς ἡ ΑΖ πρὸς ΖΕ, τουτέστιν ὡς ὁ δοθεὶς λόγος, οὕτως ἡ ἀπὸ ΑΒ∠ γωνία πρὸς τὴν ὑπὸ ∠ΒΓ, τουτέστιν ἡ ΛΜ περιφέρεια πρὸς ΜΘ.

---

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/.