# Synagoge 3.78

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.78

78 νβ΄. Τῆς ὑπὸ Ἀρχιμήδους ἐν τῷ περὶ ἑλίκων βιβλίῳ λαμβανομένης νεύσεως τὴν ἀνάλυσίν σοι κατέταξα, ἵνα τὸ βιβλίον διερχόμενος μὴ διαπορῇς. δὲ εἰς αὐτὴν οἱ ὑπογεγραμμένοι τόποι καὶ πρὸς ἄλλα πολλὰ τῶν στερεῶν προβλημάτων χρήσιμοι. Θέσει εὐθεῖα ἡ ΑΒ, καὶ ἀπὸ δοθέντος σημείου τοῦ Γ προσπιπτέτω τις ἡ Γ∠, καὶ πρὸς ὀρθὰς τῇ ΑΒ ἡ ∠Ε, ἔστω δὲ λύγος τῆς Γ∠ πρὸς ∠Ε· ὅτι τὸ Ε πρὸς ὑπερβολῇ. Ἤχθω διὰ τοῦ Γ τῇ πρὸς ὀρθὰς παράλληλος ἡ ΓΖ· δοθὲν ἄρα τὸ Ζ. καὶ τῇ ΑΒ παράλληλος ἡ ΕΗ, καὶ τῷ τῆς Γ∠ πρὸς ∠Ε λόγῳ ὁ αὐτὸς ἔστω τῆς ΓΖ πρὸς τῶν ΖΘ ΖΚ· δοθὲν ἄρα ἑκάτερον τῶν Θ Κ. ἐπεὶ οὖν ἐστιν ὡς τὸ ἀπὸ τῆς Γ∠ πρὸς τὸ ἀπὸ τῆς ∠Ε, οὕτως τὸ ἀπὸ τῆς ΓΖ πρὸς τὸ ἀπὸ τῆς ΖΘ, καὶ λοιποῦ ἄρα τοῦ ἀπὸ τῆς Ζ∠, τουτέστιν τοῦ ἀπὸ τῆς ΕΗ, πρὸς λοιπὸν τὸ ὑπὸ τῶν ΚΗΘ λόγος ἐστὶν δοθείς. καὶ ἔστι δοθέντα τὰ Κ Θ· τὸ Ε ἄρα πρὸς ὑπερβολῇ ἐρχομένῃ διὰ τῶν Θ Ε.

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Pappus Alexandrinus, Synagoge, ed. Friedrich Hultsch. 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/tlg2032.tlg001.local001/.