# Synagoge 3.7

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.7

7 Συντεθήσεται δὴ οὕτως. ἐπεὶ ὀρθή ἐστιν ἑκατέρα τῶν ὑπὸ τῶν ΕΑ∠ ΕΝ∠, ἐν κύκλῳ ἐστὶν τὰ Α ∠ E Ν σημεῖα· ἴση ἄρα ἐστὶν ἡ ὑπὸ ΑΝ∠ τῇ ὑπὸ ΑΕ∠. ἀλλʼ ἡ ὑπὸ ΑΕ∠ ἴση ἐστὶν τῇ ὑπὸ ΑΞΘ διὰ τὰς παραλλήλους τὰς Ε∠ ΞΘ ἐν κύκλῳ ἄρα τὰ Α Ν Ξ Θ σημεῖα ἴση ἄρα ἐστὶν ἡ ὑπὸ ΘΑΞ γωνία τῇ ὑπὸ ΘΝΞ. ἀλλʼ ἡ ὑπὸ ΘΑΞ ἴση ἐστὶν τῇ ὑπὸ ΘΖΜ· παράλληλος ἄρα ἐστὶν ἡ ΖΜ τῇ ΝΞ. καὶ ἔστιν ἴση ἡ ΖΝ τῇ ΝΘ· ἴση ἄρα ἐστὶν καὶ ἡ ΜΞ τῇ ΞΘ. καὶ ἔστιν ὡς ἡ ΞΗ πρὸς ΗE, οὕτως ἡ μὲν ΞΜ πρὸς ΕΚ , ἡ δέ ΘΞ πρὸς ΛΕ· καὶ ὡς ἄρα ἡ ΞΜ πρὸς ΕΚ, οὕτως ἡ ΘΞ πρὸς ΛΕ. καὶ ἐναλλάξ. καὶ ἴση ἐστὶν ἡ ΜΞ τῇ ΞΘ· ἴση ἄρα καὶ ἡ ΚΕ τῇ ΛΕ.

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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/.