# Liber assumptorum ι΄.

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/archimede/liber-assumptorum/%CE%B9%CE%84.

Εἴ κα ᾖ κύκλος καὶ δύο εὐθεῖαι αἱ △Α, △Γ ἐπιψαύουσαι αὐτοῦ κατὰ τὰ Α, Γ σαμεῖα, τέμνουσα δὲ εὐθεῖα ἁ △Β, ἀχθῇ δὲ ἁ ΕΓ παρὰ τὰν Β△, ἐπιζευχθῇ δὲ ἁ ΕΑ τέμνουσα τὰν △Β κατὰ τὸ Ζ, καὶ ἀπὸ τοῦ Ζ ποτʼ ὀρθὰς τᾷ ΕΓ ἀχθῇ ἁ ΖΗ, ἁ ἀγμένα τὰν ΕΓ δίχα τέμνει. Ἐπεζεύχθω γὰρ ἁ ΑΓ. Ἐπεὶ οὖν εὐθεῖα ἁ △Α ἐπιψαύουσα τοῦ κύκλου ἐστίν, ἁ δὲ ΑΓ τέμνουσα αὐτόν, γωνία ἁ ὑπὸ △ΑΓ τᾷ ἐν τῷ ἐναλλὰξ τμάματι τοῦ κύκλου γωνίᾳ τᾷ ὑπὸ ΑΕΓ, τουτέστι τᾷ ὑπὸ ΑΖ△, ἐστὶν ἴσα. Ἔστι γὰρ ἁ ΓΕ παρὰ τὰν Β△. Καὶ ἐπεὶ ἐν δυσὶ τριγώνοις τοῖς △ΑΖ, ΑΘ△ δύο γωνίαι αἱ ὑπὸ ΑΖ△, ΘΑ△ ἴσαι ἀλλάλαις ἐντί, γωνία δὲ ἁ πρὸς τῷ △ κοινά, τὸ ἄρα ὑπὸ τῶν Ζ△, △Θ περιεχόμενον ὀρθογώνιον τῷ ἀπὸ τᾶς △Α, τουτέστι τῷ ἀπὸ τᾶς △Γ τετραγώνῳ, ἐστὶν ἴσον ἐπεὶ οὖν ὃν λόγον ἔχει ἁ Ζ△ ποτὶ τὰν △Γ, τοῦτον ἔχει καὶ ἁ △Γ ποτὶ τὰν △Θ, γωνία δὲ ἁ ποτὶ τὸ △ σαμεῖον κοινά ἐστιν, τρίγωνα ἄρα τὰ △ΖΓ, △ΓΘ ἐστὶν ὅμοια καὶ γωνίαι αἱ ὑπὸ △ΖΓ, △ΓΘ, △ΑΘ, ΑΖ△ ἴσαι ἀλλάλαις ἐντί· ἔστι δὲ καὶ γωνία ἁ ὑπὸ △ΖΓ τᾷ ὑπὸ ΖΓΕ ἴσα· ἦν δὲ καὶ ἁ ὑπὸ △ΖΑ τᾷ ὑπὸ ΑΕΓ ἴσα ἐν δυσὶ τριγώνοις ἄρα τοῖς ΕΗΖ, ΓΗΖ δύο γωνίαι αἱ ὑπὸ ΗΕΖ, ΗΓΖ ἴσαι ἀλλάλαις ἐντὶ καὶ αἱ ποτὶ τῷ Η σαμείῳ γωνίαι ὀρθαί· ἔστι ὲ πλευρὰ ἁ ΗΖ κοινά ἔστιν ἄρα ἁ ΕΗ τᾷ ΗΓ 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/.