# Synagoge 88

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/88

88 μθ΄. Εἰς τὴν δοθεῖσαν σφαίραν κύβον ἐγγράψαι. Ἐγγεγράφθω καὶ ἔστω ἐν τῇ ἐπιφανείᾳ τῆς σφαίρας τὰ σημεῖα τῶν γωνιῶν αὐτοῦ τὰ Α Β Γ ∠ Ε Ζ Η Θ, καὶ ἐκβεβλήσθω διʼ αὐτῶν ἐπίπεδα ποιήσει δὴ τομὰς κύκλους ἴσους καὶ παραλλήλους· καὶ γὰρ τὰ ἐν αὐτοῖς τετράγωνα ἴσα τε καὶ παράλληλά ἐστιν. καὶ ἔσται ἐπεζευγμένη ἡ ΓΕ διάμετρος τῆς σφαίρσς. ἐπεζεύχθω καὶ ἡ ΕΗ. ἐπεὶ διπλάσιον τὸ ἀπὸ ΕΗ τοῦ ἀπὸ ΕΘ τουτέστιν τοῦ ἀπὸ ΗΓ, καὶ ὀρθὴ ἡ ὑπὸ ΓΗΕ γωνία, ἔσται τὸ ἀπὸ ΓΕ τοῦ ἀπὸ ΕΗ ἡμιόλιον. δοθὲν δὲ τὸ ἀπὸ ΓΕ· δοθὲν ἄρα καὶ τὸ ἀπὸ ΕΗ. καὶ ἐστιν διάμετρος τοῦ ΕΖΗΘ κύκλου· δοθεὶς ἄρα ὁ κύκλος, ὥστε καὶ ὁ ΑΒΓ∠ καὶ τὰ ἐν αὐτοῖς τετράγωνα καὶ τὰ τῶν γωνιῶν σημεῖα τοῦ κύβου.

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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/.