# Synagoge 3.71

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.71

71 μϚ΄. Ἑτέρως δὲ τέμνεται κύκλου τοῦ ΑΗΓ ἡ ΑΓ περιφέρεια. ὁμοίως ἐπὶ τὸ κέντρον αἱ ΑΒΓ, καὶ γεγράφθω διὰ τοῦ Β ἕλιξ ἡ ΒΖ∠Γ, ἧς ἡ ἐν τῇ γενέσει εὐθεῖα ἡ ΓΒ, καὶ τῷ δοθέντι λόγῳ ὁ αὐτὸς ἔοτω ὁ τῆς ∠Ε πρὸς ΕΒ, καὶ διὰ τοῦ Ε περὶ κέντρον τὸ Β κύκλου περιφέρεια ἡ ΕΖ τέμνουσα τὴν ἕλικα κατὰ τὸ Ζ, καὶ ἐπιζευχθεῖσα ἡ ΒΖ ἐκβεβλήσθω ἐπὶ τὸ Η· ἔστιν ἄρα διὰ τὴν ἕλικα ὡς ἡ ∠Β πρὸς ΒΖ, τουτέστιν πρὸς ΒΕ, οὕτως ἡ ΑΗΓ περιφέρεια πρὸς ΓΗ, καὶ διελόντι ὡς ἡ ∠Ε πρὸς ΕΒ, οὕτως ἡ ΑΗ περιφέρεια πρὸς ΗΓ. ὁ δὲ τῆς ∠Ε πρὸς ΕΒ λόγος ἐστὶν ὁ αὐτὸς τῷ δοθέντι· καὶ ὁ τῆς ΑΗ ἄρα περιφερείας πρὸς τὴν ΗΓ λόγος ὁ αὐτός ἐστιν τῷ δοθέντι· τέτμηται ἄρα: ~

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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/.