# Synagoge 3.5

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.5

καὶ ἐπεὶ τὸ μὲν ὑπὸ ∠ΗΘ ἴσον ἐστὶν τῷ ἀπὸ ΒΗ διὰ τὸ ἰσογώνια εἶναι τὰ ΒΗΘ ΒΗ∠ τρίγωνα , τὸ δὲ ὑπὸ ∠ΗΛ ἴσον ἐστὶν τῷ ἀπὸ ΚΗ διὰ τὸ ἰσογώνια εἶναι τὰ ΚΗΛ ΚΗ∠ τρίγωνα, ἔστιν ἅρα ὡς τὸ ὑπὸ ∠ΗΘ πρὸς τὸ ἀπὸ ΒΗ , οὕτως τὸ ὑπὸ ∠ΗΛ πρὸς τὸ ἀπὸ ΚΗ. καὶ ἐναλλάξ. ὡς δὲ τὸ ὑπὸ ∠ΗΘ πρὸς τὸ ὑπὸ ∠ΗΛ, οὕτως ἡ ΘΗ πρὸς τὴν ΗΛ · καὶ ὡς ἄρα ἡ ΘΗ πρὸς τὴν ΗΛ, οὕτως τὸ ἀπὸ ΒΗ, τουτέστιν τὸ ἀπὸ ΖΗ, πρὸς τὸ ἀπὸ ΗΚ· διελόντι ἄρα ἐστὶν ὡς Θ∠ πρὸς ΛΗ , οὕτως τὸ ἀπὸ ΚΖ πρὸς τὸ ἀπὸ ΗΚ. καὶ ἐδείχθη ἴσον τὸ ὑπὸ τῶν ∠ΗΛ τῷ ἀπὸ ΗΚ ἴσον ἄρα καὶ τὸ ὑπὸ τῶν ∠Η ΛΘ τῷ ἀπὸ ΚΖ. καὶ ἔστιν ἡ μὲν ΛΘ ἀποτομὴ πέμπτη, ἡ δὲ ΔΗ ῥητή· ἡ ἄρα ΚΖ ἡ μετά ῥητοῦ μέσον τὸ ὅλον ποιοῦσά ἐστιν. ἐδείχθη δὲ καὶ ἡ ∠Κ ἐκ δύο ὀνομάτων· λοιπὴ ἄρα ἡ ∠Ζ ὑπεροχή ἐστιν ἡ ὑπερέχει ἡ ἐκ δύο ὀνομάτων τῆς μετά ῥητοῦ μέσον τὸ ὅλον ποιούσης.

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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/.