# Conica λγ′.

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/apollonius-of-perga/conica/%CE%BB%CE%B3%E2%80%B2.

Ὑπερβολὴ ὑπερβολῆς τὸ αὐτὸ κέντρον ἔχουσα οὐκ ἐφάψεται κατὰ δύο σημεῖα. ὑπερβολαὶ γὰρ αἱ ΑΗΒ, ΑΜΒ τὸ αὐτὸ κέντρον ἔχουσαι τὸ Δ, εἰ δυνατόν, ἐφαπτέσθωσαν κατὰ τὰ Α, Β, ἤχθωσαν δὲ ἀπὸ τῶν Α, Β ἐφαπτόμεναι αὐτῶν καὶ συμπίπτουσαι ἀλλήλαις αἱ ΑΛ, ΛΒ, καὶ ἐπεζεύχθω ἡ ΔΛ καὶ ἐκβεβλήσθω. ἐπεζεύχθω δὴ καὶ ἡ ΑΒ· ἡ ἄρα ΔΖ τὴν ΑΒ δίχα τέμνει κατὰ τὸ Ζ. τεμεῖ. δὴ ἡ ΔΖ τὰς τομὰς κατὰ τὰ Η, Μ. ἔσται δὴ διὰ μὲν τὴν ΑΗΒ ὑπερβολὴν ἴσον τὸ ὑπὸ ΖΔΛ τῷ ἀπὸ ΔΗ, διὰ δὲ την ΑΜΒ τὸ ὑπὸ ΖΔΛ ἴσον τῷ ἀπὸ ΔΜ. τὸ ἄρα ἀπὸ ΜΔ ἴσον τῷ ἀπὸ ΔΗ· ὅπερ ἀδύνατον.

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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/.