# Synagoge 54

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/54

54 λβ΄ (ιγ΄ ). Ἐὰν ὦσιν γ΄ εὐθεῖαι ὡς αἰ Α Β Γ, ὁ κῶνος οὗ βάσις μέν ἐστιν κύκλος οὗ ἡ ἐκ τοῦ κέντρου δύναται τὸ ὑπὸ Α Β, ὕψος δὲ ἡ Γ, ἴσος ἐστὶν κώνῳ οὗ βάσις μέν ἐστιν κύκλος οὗ ἡ ἐκ τοῦ κέντρου δύναται τὸ ὑπὸ Β Γ, ὕψος δὲ ἡ Α. Ἐκκείσθωσαν γὰρ δύο κύκλοι οἱ Ε Ζ, καὶ τοῦ μὲν Ε ἡ ἐκ τοῦ κέντρου δυνάσθω τὸ ὑπὸ Α Β, τοῦ δὲ Ζ ἡ ἐκ τοῦ κέντρου δυνάσθω τὸ ὑπὸ Β Γ, ὕψος δὲ τοῦ μὲν Ε κώνου ἔστω τὸ ΕΗ ἴσον τῇ Γ, τοῦ δὲ Ζ ὕψος τὸ ΖΘ ἴσον ἔστω τῇ Α. ἐπεὶ οὖν ἐστιν ὡς ἡ Α πρὸς Γ, τουτέστιν ὡς ἡ ΖΘ πρὸς τὴν ΕΗ, τὸ ὑπὸ Α Β πρὸς τὸ ὑπὸ B Γ , τουτέστιν ὁ Ε πρὸς τὸν Ζ, ἴσος ἄρα ὁ κῶνος οὗ βάσις μὲν ὁ Ε κύκλος, ὕψος δὲ τὸ ΕΗ, τῷ κύνῳ οὗ βόσις μὲν ὁ Ζ κύκλος, ὕψος δὲ τὸ ΖΘ· ἀντιπεπόνθασιν γάρ αὐτῶν αἱ βάσεις τοῖς ὕψεσιν.

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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/.