# Optica κ΄.

Euclid, Optica, κ΄.. Ancient Greek.

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

Τὸ δοθὲν βάθος γνῶναι, πηλίκον ἐστίν. ἔστω τὸ δοθὲν βάθος τὸ Α∠, ὄμμα δὲ ἔστω τὸ Ε, καὶ δέον τὸ βάθος γνῶναι, πηλίκον ἐστίν. προσπιπτέτω γὰρ τῇ ὄψει ἡλίου ἀκτὶς ἡ Ε∠ συμβάλλουσα τῷ ἐπιπέδῳ κατὰ τὸ Β σημεῖον καὶ τῷ βάθει κατὰ τὸ ∠. καὶ προσεκβεβλήσθω ἀπὸ τοῦ Β ἐπʼ εὐθείας ἡ ΒΖ, καὶ ἤχθω ἀπὸ τοῦ Ε ἐπὶ τὴν ΒΖ εὐθεῖαν κάθετος ἡ ΕΖ. ἐπεὶ οὖν ἴση γωνία ἡ ὑπὸ ΕΖΒ τῇ ὑπὸ ΒΑ∠, ἀλλὰ καὶ ἡ ὑπὸ ΑΒ∠ τῇ ὑπὸ ΕΒΖ, καὶ ἡ τρίτη ἄρα ἡ ὑπὸ ΒΕΖ τῇ ὑπὸ Α∠Β ἐστιν ἴση. ἰσογώνιον ἄρα ἐστὶ τὸ Α∠Β τρίγωνον τῷ ΒΕΖ τριγώνῳ. καὶ αἰ πλευραὶ ἄρα ἀνάλογον ἔσονται. ἔστιν ἄρα, ὡς ἡ ΕΖ πρὸς τὴν ΖΒ, ἡ ∠Α πρὸς τὴν ΑΒ. ἀλλʼ ὁ τῆς ΕΖ πρὸς τὴν ΖΒ λόγος ἐστὶ γνώριμος· καὶ ὁ τῆς ∠Α ἄρα πρὸς τὴν ΑΒ λόγος ἐστὶ γνώριμος. καί ἐστι καὶ τὸ ΑΒ γνώριμον. καὶ τὸ Α∠ ἄρα γνώριμόν ἐστιν.

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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/.