# Synagoge 14-2

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/14-2

14 β΄. Ἔστω τις εὐθεῖα ἡ ΑΗ τετμημένη εἰς ἴσα κατὰ τὰ B Γ ∠ Ε Ζ· ὅτι ἐστὶν ὡς ἡ ΑΓ πρὸς ΓΒ, ἡ BΓ πρὸςτ τὸ ἥμισυ τῆς ΒΓ, ὡς δὲ ἡ Α∠ πρὸς ∠Β. οὕτως ἡ Β∠ πρὸς τὴν ∠Γ καὶ τὸ τρίτον τῆς ΓΒ, ὡς δὲ ἡ ΑΕ πρὸς ΕΒ, οὕτως ἡ ΒΕ πρὸς τὴν ΕΓ καὶ τὸ τέταρτον τῆς ΓΒ, ὡς δὲ ἡ ΑΖ πρὸς τὴν ΖΒ, οὕτως ἡ ΒΖ πρὸς τὴν ΖΓ καὶ τὸ πέμπτον τῆς ΓΒ, ὡς δὲ ἡ ΑΗ πρὸς τὴν ΗΒ, οὕτως ἡ 8Η πρὸς τὴν ΗΓ καὶ τὸ ἕκτον τῆς ΓΒ. Ἔστι δὲ φανερὸν τῶν ἀριθμῶν παραληφθέντων καὶ ἀεὶ οὕτως, ὅτι ὡς ὁ δοθεὶς τῶν ἴσων εὐθειῶν ἀριθμὸς ἀπὸ τοῦ Α πρὸς τὸν μονάδι ἐλάσσονα, οὕτως ὁ μονάδι ἐλάσσων πρὸς τὸν μονάδι αὐτοῦ ἐλάσσονα καὶ τῆς ΓΒ μόριον ὁμώνυμον τῷ δοθέντι πλήθει τῶν ἴσων εὐθειῶν.

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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/.