# Fragmenta 6.25

Euclid, Fragmenta, Chapter 6. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/6.25

κε΄. Ἔστω τὸ ὑπὸ τῶν ΑΒΓ ἴσον τῷ ἀπὸ τῆς Β∠· ὅτι γίνεται γ, τὸ μὲν ὑπὸ τῆς τῶν Α∠, ∠Γ ὑπεροχῆς καὶ τῆς Β∠ ἴσον τῷ ὑπὸ Α∠Γ τὸ δὲ ὑπὸ τῆς τῶν Α∠Γ ὑπεροχῆς καὶ τῆς ΒΓ ἴσον τῷ ἀπὸ τῆς ∠Γ τετραγώνῳ, τὸ δὲ ὑπὸ τῆς τῶν Α∠, ∠Γ ὑπεροχῆς καὶ τῆς ΒΑ ἴσον τῷ ἀπὸ τῆς Α∠ τετραγώνῳ. ἐπεὶ γάρ ἐστιν, ὡς ἡ ΑΒ πρὸς τὴν Β∠, οὕτως ἡ Β∠ πρὸς τὴν ΒΓ, λοιπὴ πρὸς λοιπὴν καὶ διελόντι· ἔστιν οὖν, ὡς ἡ τῶν Α∠, ∠Γ ὑπεροχὴ πρὸς τὴν ∠Γ, οὕτως ἡ Α∠ πρὸς τὴν ∠Β τὸ ἄρα ὑπὸ τῆς τῶν Α∠, ∠ ὑπεροχῆς καὶ τῆς ∠Β ἴσον ἐστὶν τῷ ὑπὸ τῶν Α∠, ∠Γ. πάλιν, ἐπεὶ λοιπὴ ἡ Α∠ πρὸς λοιπὴν τὴν ∠Γ ἐστιν, ὡς ἡ ∠Β πρὸς τὴν ΒΓ, διελόντι ἐστίν, ὡς ἡ τῶν Α∠Γ ὑπεροχὴ πρὸς τὴν ∠Γ, οὕτως ἡ ∠Γ πρὸς τὴν ΓΒ· τὸ ἄρα ὑπὸ τῆς τῶν Α∠, ∠Γ ὑπεροχῆς καὶ τῆς ΒΓ ἴσον ἐστὶν τῷ ἀπὸ τῆς ΔΓ τετραγώνῳ. πάλιν, ἐπεί ἐστιν, ὡς ἡ Α∠ πρὸς τὴν ∠Γ οὕτως ἡ ΑΒ πρὸς τὴν Β∠, ἀνάπαλιν καὶ διελόντι ἐστίν, ὡς ἡ τῶν Απαλιν, ∠Γ ὑπεροχὴ πρὸς τὴν ∠Α, οὕτως ἡ ∠Α πρὸς τὴν ΑΒ τὸ ἄρα ὑπὸ τῆς τῶν Α∠, ∠Γ ὑπεροχῆς καὶ τῆς ΑΒ ἴσον ἐστὶν τῷ ἀπὸ τῆς Α∠ τετραγώνῳ.

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Euclid, Fragmenta, ed. Heinrich Menge. 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/tlg1799.tlg016.local001/.