# Synagoge 3.66

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.66

66 μβ΄. Συντεθήσεται δὴ οὕτως. ἔστωσαν αἱ μὲν τῇ θέσει δοθεῖσαι εὐθεῖαι αἱ ΑΒΓ, τὸ δὲ δοθὲν σημεῖον τὸ ∠, καὶ τῇ μὲν ΒΓ παράλληλος ἤχθω ἡ ∠Θ, τῇ δὲ ΒΘ ἴση ἡ ΘΑ, καὶ ἐπιζευχθεῖσα ἡ Α∠ ἐκβεβλήσθω ἐπὶ τὸ Γ, ἐπιζευχθεῖσα δέ καὶ ἡ Β∠ ἐκβεβλήσθω καὶ τῇ Β∠ ἴση κείσθω ἡ ΒΗ, καὶ τῷ ἀπὸ τῆς ΑΓ ἴσον ἔστω τὸ ὑπὸ τῆς Η∠ καὶ ἑτέρας τινὸς τῆς Κ, καὶ περὶ διάμετρον τὴν Η∠ καὶ ὀρθίαν τὴν Κ γεγράφθω ὑπερβολὴ ἡ Ε∠Ζ , ὥστε τὰς καταγομένας ἐπὶ τὴν Η∠ παραλλήλους εἶναι τῇ ΑΓ· ἡ ἄρα ΑΓ ἐφάπτεται τῆς τομῆς. καὶ ἔστιν ἡ Α∠ τῇ ∠Γ ἴση (ἐπεὶ καὶ ἡ ΒΘ τῇ ΘΑ) , καὶ φανερὸν ὅτι τὸ ἀφ᾿ ἑκατέρας τῶν Α∠ ∠Γ τέταρτόν ἐστι τοῦ πρὸς τῇ Η∠ εἴδους· αἱ ἄρα ΑΒΓ ἀσύμπτωτοί εἰσι τῆς Ε∠Ζ ὑπερβολῆς· γέγραπται ἅρα διὰ τοῦ ∠ περὶ τὰς δοθείσας εὐθείας ἀσυμπτώτους ὑπερβολή.

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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/.