# Conica λ′.

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

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

Παραβολὴ παραβολῆς οὐκ ἐφάψεται κατὰ πλείονα σημεῖα ἢ ἕν. εἰ γὰρ δυνατόν, ἐφαπτέσθωσαν αἱ ΑΗΒ, ΑΜΒ παραβολαὶ κατὰ τὰ Α, Β, καὶ ἤχθωσαν ἐφαπτόμεναι αἱ ΑΛ, ΛΒ· ἐφάψονται δὴ αὗται τῶν τομῶν ἀμφοτέρων καὶ συμπεσοῦνται κατὰ τὸ Λ. ἐπεζεύχθω ἡ ΑΒ καὶ δίχα τετμήσθω κατὰ τὸ Ζ, καὶ ἤχθω ἡ ΛΖ. ἐπεὶ οὖν δύο γραμμαὶ αἱ ΑΗΒ, ΑΜΒ ἐφάπτονται ἀλλήλων κατὰ δύο τὰ Α, Β, οὐ συμβάλλουσιν ἀλλήλαις καθ’ ἕτερον· ὥστε ἡ ΛΖ ἑκατέραν τῶν τομῶν τέμνει. τεμνέτω κατὰ τὰ Η, Μ· ἔσται δὴ διὰ μὲν τὴν ἑτέραν τομὴν ἡ ΛΗ τῇ ΗΖ ἴση, διὰ δὲ τὴν ἑτέραν ἡ ΛΜ τῇ ΜΖ ἴση· ὅπερ ἀδύνατον. οὐκ ἄρα παραβολὴ παραβολῆς ἐφάψεται κατὰ πλείονα σημεῖα ἢ ἕν.

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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/.