# Conica κγ′.

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

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

Ἔστωσαν πάλιν ἀντικείμεναι αἱ Α, Β, καὶ τὸ Δ σημεῖον ἐν τῇ ἐφεξῆς γωνίᾳ τῆς ὑπὸ τῶν ἀσυμπτώτων περιεχομένης, καὶ ἡ μὲν ΒΔ ἤχθω τὴν Β τομὴν καθ’ ἓν μόνον τέμνουσα, τῇ δὲ ἑτέρᾳ τῶν ἀσυμπτώτων παράλληλος, ἡ δὲ ΔΑ τὴν Α τομὴν ὁμοίως, καὶ ἔστω ἴση ἡ μὲν ΔΒ τῇ ΒΗ, ἡ δὲ ΔΑ τῇ ΑΚ. λέγω, ὅτι ἡ διὰ τῶν Κ, Η συμβάλλει ταῖς τομαῖς, καὶ αἱ ἀπὸ τῶν συμπτώσεων ἐπὶ τὸ Δ ἀγόμεναι ἐφάψονται τῶν τομῶν. ἤχθωσαν ἐφαπτόμεναι αἱ ΔΕ, ΔΖ, καὶ ἐπιζευχθεῖσα ἡ ΕΖ, εἰ δυνατόν, μὴ ἐρχέσθω διὰ τῶν Κ, Η. ἤτοι δη διὰ τοῦ ἑτέρου αὐτῶν ἐλεύσεται ἢ δι’ οὐδετέρου, καὶ ἤτοι ἡ ΔΑ οὐκ ἔσται ἴση τῇ ΑΚ, ἀλλὰ ἄλλη τινί· ὅπερ ἄτοπον· ἢ ἡ ΔΒ τῇ ΒΗ οὐκ ἴση, ἢ οὐδετέρα οὐδετέρᾳ, καὶ πάλιν ἐπ’ ἀμφοτέρων τὸ αὐτὸ ἄτοπον συμβήσεται. ἥξει ἄρα ἡ ΕΖ διὰ τῶν Κ, Η.

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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/.