# Data β΄.

Euclid, Data, β΄.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/data/%CE%B2%CE%84.

Ἐὰν δεδομένον μέγεθος πρὸς ἄλλο τι μέγεθος λό- γον ἔχῃ δεδομένον, δέδοται κᾀκεῖνο τῷ μεγέθει. δεδομένον γὰρ μέγεθος τὸ Α πρὸς ἄλλο τι μέγεθος τὸ Β λόγον ἐχέτω δεδομένον· λέγω, ὅτι δέδοται καὶ τὸ Β τῷ μεγέθει. ἐπεὶ γὰρ δέδοται τὸ Α, δυναπτόν ἐστιν αὐτῷ ἴσον πορίσασθαι. πεπορίσθω καὶ ἔστω τὸ Γ. καὶ ἐπεὶ δέδοται ὁ τοῦ Α πρὸς τὸ Β λόγος· οὕτως γὰρ ὑπό- κειται· δυνατόν ἐστιν αὐτῷ τὸν αὐτὸν πορίσασθαι. πεπορίσθω καὶ ἔστω ὁ τοῦ Γ πρὸς τὸ Δ λόγος. καὶ ἐπεί ἐστιν ὡς τὸ Α πρὸς τὸ Β, οὕτως τὸ Γ πρὸς τὸ Δ, ἐναλλὰξ ἄρᾳ ἐστὶν ὡς τὸ Α πρὸς τὸ Γ, οὕτως τὸ Β πρὸς τὸ Δ. ἴσον δὲ τὸ Α τῷ Γ· ἴσον ἄρα καὶ τὸ Β τῷ Δ· δέδοται ἄρα τὸ Β μέγεθος· ἴσον γὰρ αὐτῷ πεπόρισται τὸ Δ.

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Euclid, Data, 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.tlg007.local001/.