# Conica κζ′.

Apollonius of Perga, Conica, κζ′.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/apollonius-of-perga/conica/%CE%BA%CE%B6%E2%80%B2.

Ἐὰν τῶν προειρημένων γραμμῶν τινες κατὰ δύο σημεῖα ἐφάπτωνται ἀλλήλων, οὐ συμβάλλουσιν ἀλλήλαις καθ’ ἕτερον. δύο γὰρ τῶν εἰρημένων γραμμῶν ἐφαπτέσθωσαν ἀλλήλων κατὰ δύο σημεῖα τὰ Α, Β. λέγω, ὅτι ἀλλήλαις κατὰ ἄλλο σημεῖον οὐ συμβάλλουσιν. εἰ γὰρ δυνατόν, συμβαλλέτωσαν καὶ κατὰ τὸ Γ, καὶ ἔστω πρότερον τὸ Γ ἐκτὸς τῶν Α, Β ἁφῶν, καὶ ἤχθωσαν ἀπο τῶν Α, Β ἐφαπτόμεναι· ἐφάψονται ἄρα ἀμφοτέρων τῶν γραμμῶν. ἐφαπτέσθωσαν καὶ συμπιπτέτωσαν κατὰ τὸ Λ, ὡς ἐπὶ τῆς πρώτης καταγραφῆς, καὶ ἐπεζεύχθω ἡ ΓΛ· τεμεῖ δὴ ἑκατέραν τῶν τομῶν. τεμνέτω κατὰ τὰ Η, Μ, καὶ ἐπεζεύχθω ἡ ΑΝΒ. ἔσται ἄρα ἐν μὲν τῇ ἑτέρᾳ τομῇ, ὡς ἡ ΓΛ πρὸς ΛΗ, ἡ ΓΝ πρὸς ΝΗ, ἐν δὲ τῇ ἑτέρᾳ, ὡς ἡ ΓΛ πρὸς ΛΜ, ἡ ΓΝ πρὸς ΝΜ· ὅπερ ἄτοπον.

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Apollonius of Perga, Conica, ed. J. L. Heiberg. 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/tlg0550.tlg001.local001/.