# Optica κα΄.

Euclid, Optica, κα΄.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/optica/%CE%BA%CE%B1%CE%84.

Τὸ δοθὲν μῆκος ἐπιγνῶναι, πηλίκον ἐστίν. ἔστω τὸ δοθὲν μῆκος τὸ ΑΒ, ὄμμα δὲ ἔστω τὸ Γ. καὶ δέον ἔστω τὸ ΑΒ μῆκος γνῶναι, πηλίκον ἐστίν προσπιπτέτωσαν ἀκτῖνες αἱ ΓΑ, ΓΒ, καὶ εἰλήφθω ἐγγὺς τοῦ ὄμματος τοῦ Γ ἐπὶ τῆς ἀκτῖνος τυχὸν σημεῖον τὸ ∠, καὶ ἤχθω διὰ τοῦ ∠ σημείου τῇ ΑΒ παράλληλος εὐθεῖα ἡ ∠Ε. ἐπεὶ οὖν τριγώνου τοῦ ΑΒΓ παρὰ μίαν τῶν πλευρῶν τὴν ΒΑ ἦκται ἡ ∠Ε, ἔστιν ἄρα, ὡς ἡ Γ∠ πρὸς τὴν ∠Ε, οὕτως ἡ πρὸς τὴν ΑΒ. ἀλλʼ ὁ τῆς Γ∠ πρὸς τὴν ∠Ε λόγος ἐστὶ γνώριμος· καὶ ὁ τῆς ΑΓ ἄρα πρὸς τὴν ΑΒ λόγος γνώριμός ἐστιν. καὶ γνώριμός ἐστιν ἡ ΑΓ. γνώριμος ἄρα καὶ ἡ ΑΒ.

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Euclid, Optica, ed. Johan Ludvig Heiberg, 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.tlg009.local001/.