# Synagoge 48-2

Pappus Alexandrinus, Synagoge, ΠΑΠΠΟΥ ΑΛΕΞΑΝΔΡΕΩΣ ΣΥΝΑΓΩΓΗΣ Ε.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/48-2

48 ἀλλὰ τῷ δὶς ὑπὸ ΡΗΘ καὶ τῷ ὑπὸ ΗΘΚ ἴσον ἐστὶν τὸ ὑπὸ συναμφοτέρου τῆς ΗΡΚ καὶ τῆς ΗΘ μετὰ τοῦ ἀπὸ ΗΘ (τοῦτο γὰρ ἑξῆς δειχθήσεται). καὶ τὸ ἄρα ἀπὸ ΑΗ ὑπὸ ΖΗΘ, ὡς ἔχει ἐπὶ τῆς δευτέρας καταγραφῆς, πάλιν τὸ ὑπὸ ΚΘΗ ἴσον γίνεται τῷ ἡμίσει τοῦ ἀπὸ τῆς ἐπὶ τὰ Ζ Θ οὕτως· ἐπεὶ τὸ ἀπὸ ΖΘ μεῖζόν ἐστιν τῶν ἀπὸ ΖΗ ΗΘ τῷ δὶς ὑπὸ ΘΗΚ , καὶ τὸ ἥμισυ ἄρα τοῦ ἀπὸ τῆς ἐπὶ τὰ Θ τοῦ ἀπὸ ΗΘ μεῖζόν ἐστιν τῷ ὑπὸ ΘΗΚ. τὸ ἄρα ἀπὸ ΘΗ μετὰ τοῦ ὑπὸ ΘΗΚ ἄσον ἐστὶν τῷ ἡμίσει τοῦ ἀπὸ τῆς ἐπὶ τὼ Ζ Θ. τῷ δέ ἀπὸ ΘΗ μετὰ τοῦ ὑπὸ ΘΗΚ ἴσον ἐστὶν τὸ ὑπὸ ΚΘΗ διὰ τὸ γʼ τοῦ β΄ στοιχείων· καὶ τὸ ἥμισυ ἄρα τοῦ ἀπὸ τῆς ἐπὶ τὼ Ζ Θ ἄσον ἐστὶν τῷ ὑπὸ ΚΘΗ. Καὶ ἐπεὶ τὸ ἥμισυ εοῦ ἀπὸ τῆς ἐπὶ τὰ Ζ Θ ἔλασσόν ἐστιν ἀεὶ τοῦ δὶς ἀπὸ Ζ H, δῆλον ὡς ἡ ὑπὸ τῶν AΓ Γ∠ ∠Ε ΕΖ ΖΗ γινομένη ἐπιφάνεια τοῦ κύκλου οὗ ἡ ἐκ τοῦ κέντρου ἐστὶν ἡ ΑΗ μετὰ δύο κύκλων, ὧν ἐκ κέντρου ἐστὶν ἡ ΖΗ, ἐλάσσων ἐστίν.

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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/.