# Conica κα′.

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

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

Ἔστωσαν πάλιν ἀντικείμεναι αἱ Α, Β, καὶ τὸ Δ σημεῖον ἐπὶ μιᾶς τῶν ἀσυμπτώτων, καὶ ἡ μὲν ΔΒΚ τῇ τομῇ καθ’ ἓν μόνον σημεῖον συμβαλλέτω τὸ Β παράλληλος οὖσα τῇ ἑτέρᾳ τῶν ἀσυμπτώτων, ἡ δὲ ΓΔΘ ἑκατέρᾳ τῶν τομῶν συμβαλλέτω, καὶ ἔστω, ὡς ἡ ΓΔ πρὸς ΔΘ, ἡ ΓΗ πρὸς ΗΘ, τῇ δὲ ΔΒ ἴση ἔστω ἡ ΒΚ. λέγω, ὅτι ἡ διὰ τῶν Κ, Η σημείων συμπεσεῖται τῇ τομῇ καὶ παράλληλος ἔσται τῇ ἀσυμπτώτῳ, ἐφ’ ἧς ἐστι τὸ Δ σημεῖον, καὶ ἡ ἀπὸ τῆς συμπτώσεως ἐπὶ τὸ Δ ἀγομένη ἐφάψεται τῆς τομῆς. ἤχθω γὰρ ἐφαπτομένη ἡ ΔΖ, καὶ ἀπὸ τοῦ Ζ παρὰ τὴν ἀσύμπτωτον, ἐφ’ ἧς ἐστι τὸ Δ, ἤχθω εὐθεῖα· ἥξει δὴ διὰ τῶν Κ, Η. εἰ γὰρ μή, τὰ πρότερον εἰρημένα ἄτοπα συμβήσεται.

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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/.