# Synagoge 67-2

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/67-2

67 μα΄. (κβ΄). Ἔστω δέ ἐλάσσων τῆς σφαίρας ὁ εἰρημένος κῶνος, οὗ βάσις μέν ἐστι κύκλος οὗ ἡ ἐκ τοῦ κέντρου ἐστὶν ἡ ΑΒ, ὕψος δὲ ἡ ΓΒ, τουτέστιν οὗ βάσις μέν ἐστιν κύκλος οὗ ἡ ἐκ τοῦ κέντρου δύναται τὸ ὑπὸ ΑΒΓ, ὕψος δὲ ἡ ΑΒ , καὶ μεταξὺ τῆς σφαίρας καὶ τοῦ κώνου νοείσθω κῶνος οὗ βάσις μέν ἐστιν ἡ αὐτή, ὕψος δέ ἡ Κ μείζων τῆς ΑΒ, καὶ περιγεγράφθω περὶ τὸ ἡμικύκλιεν πολύγωνον ἰσόπλευρον, ὥστε μίαν αὐτοῦ πλευρὰν τὴν ∠Ε τῆς ὐπεροχῆς τῶν Κ ΑΒ ἔλάσσονα εἶναι. καὶ ἔστιν μείζων ἡ ∠Ε τῶν ∠Α ΒΜ, ἐπεὶ καὶ ἡ Ν∠ τῆς ∠Α καὶ ἡ ∠Μ ἄρα τῆς Κ 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/.