# Liber assumptorum β΄.

Archimède, Liber assumptorum, β΄.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/archimede/liber-assumptorum/%CE%B2%CE%84.

Ἔστω ἁμικύκλιον τὸ ΑΒΓ καὶ δύο εὐθεῖαι ἐπιψαύουσαι αὐτοῦ αἱ △Β, △Γ, ἁ δὲ ΒΕ ἄχθω ποτʼ ὀρθὰς τᾷ ΑΓ, ἐπεζεύχθω δὲ ἁ Α△· φαμὶ δὴ τὰν ΒΖ ἴσαν εἶμεν τᾷ ΖΕ. Ἐπεζεύχθω γὰρ ἁ ΑΒ καὶ ἐκβληθεῖσαι αἱ ΑΒ, Γ△ συμπιπτέτωσαν κατὰ τὸ Η σαμεῖον καὶ ἄχθω ἁ ΒΓ. Ἐπεὶ οὖν γωνία ἁ ὑπὸ ὀρθά ἐστιν, ἐσσεῖται καὶ γωνία ἁ ὑπὸ ΓΒΗ ὀρθά ἔστι δὲ καὶ εὐθεῖα ἁ Β△ τᾷ △Γ ἴσα· ἐσσεῖται ἄρα καὶ εὐθεῖα ἁ △Η τᾷ △Β, τουτέστι τᾷ △Γ ἴσα. Καὶ ἐπεὶ ἁ ΒΕ παρὰ τὰν ΗΓ ἐστίν, ἐσσεῖται ἄρα καὶ ἁ ΒΖ τᾷ ΖΕ ἴσα· δέδεικται οὖν τὸ προτεθέν.

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Archimède, Liber assumptorum, ed. Charles Mugler. 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/tlg0552.tlg011.local001/.