# Conica να′.

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/apollonius-of-perga/conica/%CE%BD%CE%B1%E2%80%B2.

Ἐὰν ὑπερβολὴ ἑκατέρας τῶν ἀντικειμένων ἐφάπτηται, ἡ ἀντικειμένη αὐτῇ οὐδεμιᾷ τῶν ἀντικειμένων συμπεσεῖται. ἔστωσαν ἀντικείμεναι αἱ Α, Β, καὶ ὑπερβολὴ ἡ ΑΒ ἑκατέρας αὐτῶν ἐφαπτέσθω κατὰ τὰ Α, Β, ἀντικειμένη δὲ αὐτῆς ἔστω ἡ Ε. λέγω, ὅτι ἡ Ε οὐδετέρᾳ τῶν Α, Β συμπεσεῖται. εἰ γὰρ δυνατόν, συμπιπτέτω τῇ Α κατὰ τὸ Δ, καὶ ἤχθωσαν ἀπὸ τῶν Α, Β ἐφαπτόμεναι τῶν τομῶν· συμπεσοῦνται δὴ ἀλλήλαις ἐντὸς τῶν ἀσυμπτώτων τῆς ΑΒ τομῆς. συμπιπτέτωσαν κατὰ τὸ Γ, καὶ ἐπεζεύχθω ἡ ΓΔ· ἡ ἄρα ΓΔ ἐν τῷ μεταξὺ τόπῳ ἔσται τῶν ΑΓ, ΓΒ. ἀλλὰ καὶ μεταξὺ τῶν ΒΓ, ΓΖ· ὅπερ ἄτοπον. οὐκ ἄρα ἡ Ε συμπεσεῖται ταῖς Α, Β.

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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/.