# Synagoge 3.28

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.28

28 ιθ´ Τὸ ὑπερτεθὲν λῆμμα. ἡμικύκλια τὰ BΗΓ ΒΑ∠, καὶ ἀρθὴ ἡ ∠Ε, καὶ κύκλος ἐφαπτόμενος ὁ ΘΗΖΑ· ὅτι ἐστὶν ὡς ἡ ΒΓ πρὸς τὴν Γ∠ μήκει, οὕτως ἡ ∠Ζ πρὸς τὴν διάμετρον τοῦ ΘΗΖΑ κύκλου δυνάμει. Ἤχθω διάμετρος ἡ ΘΖ· εὐθεῖαι ἄρα αἱ ΖΑΒ ΘΑ∠. κάθετος ἤχθω ἡ ΘΚ· ἔσται ἄρα διὰ τὰ προδεδειγμένα τὸ ὑπὸ τῶν ΓΒ ΒΚ περιεχόμενον χωρίον ἴσον τῷ ἀπὸ τῆς1Β∠ τετραγώνῳ ὡς ἄρα ἡ ΒΓ πρὸς ΓΒ∠, οὕτως ἡ ΒΒ∠ πρὸς Β∠Κ, τουτέστιν πρὸς ΘΖ. ὡς δὲ ἡ ΒΒ∠ πρὸς ΘΖ, ἡ Β∠Α πρὸς ΘΑ, ὡς δὲ ἡ Β∠Α πρὸς ΑΘ, οὕτως τὸ ἀπὸ τῆς Ζ∠ πρὸς τὸ ἀπὸ τῆς ΘΖ (ὀρθογώνιον γάρ ἐστιν τὸ ΘΖ∠, καὶ κάθετος ἐπὶ τὴν ὑποτείνουσαν ἡ ΖΑ)· καὶ ὡς ἄρα ἡ ΒΓ πρὸς Γ∠, οὕτως τὸ ἀπὸ τῆς Ζ∠ πρὸς τὸ ἀπὸ τῆς διαμέτρου τοῦ ΘΗΖΑ κύκλου.

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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/.