# Synagoge 3.49

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.49

49 λβ΄. Λέγω δέ ὅτι οὐδέ πρὸς ἐλάσσονα. εἰ γὰρ δυνατόν, ἔστω πρὸς τὴν ΚΓ, καὶ περὶ κέντρον τὸ Γ περιφέρεια γεγράφθω ἡ ΖΜΚ, καὶ πρὸς ὀρθὰς τῇ Γ∠ ἡ ΚΗ τέμνουσα τὴν τετραγωνίζουσαν κατὰ τὸ Η, καὶ ἐπιζευχθεῖσα ἡ ΓΗ ἐκβεβλήσθω ἐπὶ τὸ Ε. ὁμοίως δὴ τοῖς προγεγραμμένοις δείξομεν καὶ τὴν ΖΜΚ περιφέρειαν τῇ ΒΓ εὐθείᾳ ἴσην , καὶ ὡς τὴν ΒΕ∠ περιφέρειαν πρὸς τὴν Ε∠ τουτἐστιν ὡς τὴν ΖΜΚ πρὸς τὴν ΜΚ , πὕτως τὴν ΒΓ εὐθεῖαν πρὸς τὴν ΗΚ. ἐξ ὧν φανερὸν ὅτι ἴση ἔσται ἡ ΜΚ περιφέρεια τῇ ΚΗ εὐθείᾳ , ὅπερ ἄτοπον. οὖκ ἄρα ἔσται ὡς ἧ ΒΕ∠ περιφέρεια πρὸς τὴν ΒΓ ἐθεῖαν, οὕτως ἡ ΒΓ πρὸς ἐλάσσονα τῆς ΓΘ. ἐδείχθη δέ ὅτι οὐδὲ πρὸς μείζονα· πρὸς αὐτὴν ἄρα τὴν ΓΘ.

---

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/.