# Synagoge 3.75

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.75

75 Πῶς δ᾿ εὑρίσκεται κύκλος οὗ ἡ περιφέρεια ἴση ἐστὶ τῇ δοθείσῳ εὐθείᾳ, συνιδεῖν εὔκολον. Εὑρήσθω γὰρ τῇ Γ εὐθείᾳ ἴση ἡ τοῦ Α κύκλου περιφέρεια, καὶ ἐκκείσθω κύκλος τυχὼν ὁ Β, καὶ τῇ περιφερείᾳ αὐτοῦ ἴση διὰ τῆς τετραγωνιζούσης εὑρήσθω ἡ ∠ εὐθεῖα. ἔστιν ἄρα ὡς ἡ Γ πρὸς τὴν ∠, οὕτως ἡ ἐκ τοῦ κέντρου τοῦ Α κύκλου πρὸς τὴν ἐκ τοῦ κέντρου τοῦ Β. λόγος δὲ τῆς ∠ πρὸς Γ· λόγος ἄρα καὶ τῶν ἐκ τοῦ κέντρου πρδς ἀλλήλας. καὶ ἔστιν δοθεῖσα ἡ ἐκ τοῦ κέντρου τοῦ Β· δοθεῖσα ἄρα καὶ ἡ ἐκ τοῦ κέντρου τοῦ Α, ὥστε καὶ αὐτὸς ὁ Α. καὶ φανερὰ ἡ σύνθεσις.

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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/.