# Commentarii in libros de sphaera et cylindro Εἰς τὸ γ΄.-2

Eutocius, Commentarii in libros de sphaera et cylindro, Εἰς τὸ γ΄.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/eutocius/commentarii-in-libros-de-sphaera-et-cylindro/%CE%95%E1%BC%B0%CF%82%20%CF%84%E1%BD%B8%20%CE%B3%CE%84.-2

Ὡς δὲ οἱ εἰρημένοι κύκλοι πρὸς ἀλλήλους, τὸ ἀπὸ Α∠ πρὸς τὸ ἀπὸ △Β, τουτέστιν ἡ ΑΓ πρὸς ΓΒ | Ὡς γὰρ ἐν αὐτῇ τῇ τοῦ ῥητοῦ καταγραφῇ, ἐπεὶ ἐν ὀρθογωίῳ τριγώνῳ τῷ Α△Β κάθετος ἦκται καὶ ἀπὸ τῆς ὀρθῆς ἡ △Γ, μέση ἀνάλογόν ἐστι τῶν τῆς βάσεως τμημάτων, καὶ τὰ πρὸς τῇ καθέτῳ τρίγωνα ὅμοιά ἐστι τῷ τε ὅλῳ καὶ ἀλλήλοις ὥστ᾿ ἐστὶν ὡς ἡ ΒΓ πρὸς △Γ, ἡ Β△ πρὸς △Α· καὶ τὰ ἀπ᾿ αὐτῶν ἄρα. Ἀλλ᾿ ὡς τὸ ἀπὸ ΒΓ πρὸς τὸ ἀπὸ Γ△, οὕτως ἡ πρώτη ἡ ΒΓ πρὸς τρίτην τὴν ΓΑ· καὶ ὡς ἄρα ἡ ΒΓ πρὸς ΓΑ, τὸ ἀπὸ Β△ πρὸς τὸ ἀπὸ △Α. Δοθεὶς δὴ λόγος τῆς ΑΓ πρὸς ΓΒ· ὥστε δοθὲν ἐστι τὸ Γ σημεῖον | Ἐπεὶ γὰρ ἡ σφαῖρα ὑπόκειται δεδομένη, δέδοται ἄρα καὶ ἡ διάμετρος αὐτῆς ἡ ΑΒ. Καὶ δέδοται ὁ λόγος τῆς ΑΓ πρὸς ΓΒ· ἐὰν δὲ δεδομένον μέγεθος εἰς δεδομένον λόγον διαιρεθῇ, δέδοται ἑκάτερον τῶν τμημάτων· ὥσθε δοθεῖσά ἐστιν ἡ ΑΓ. Καὶ δοθὲν τὸ Α· ἐπὶ γὰρ τῆς κοινῆς τομῆς ἐστι θέσει δεδομένων γραμμῶν δέδοται ἄρα καὶ τὸ Γ.

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Eutocius, Commentarii in libros de sphaera et cylindro, 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/tlg4072.tlg001.local001/.