# Fragmenta 12.1

Euclid, Fragmenta, Chapter 12. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/12.1

12. Archimedes Περὶ κωνοειδ. καὶ σφαιροειδ. prop.3 (I p. 27Ο, 15 sqq.): Εἰ κα κώνου τομᾶς ὁποιασοῦν εὐθεῖαι ἐπιψαύωντι ἀπὸ τοῦ αὐτοῦ σαμείου ἀγμέναι, ἔωντι δὲ καὶ ἄλλαι εὐθεῖαι ἐν τᾷ τοῦ κώνου τομᾷ παρὰ τὰς ἐπιψαυούσας ἀγμέναι καὶ τέμνουσαι ἀλλάλας, τὰ περιεχόμενα ὑπὸ τῶν τμαμάτων τὸν αὐτὸν ἑξοῦντι λόγον ποτ᾿ ἄλλαλα, ὃν τὰ τετράγωνα τὰ ἀπὸ τᾶν ἐπιψαυουσᾶν· ὁμόλογον δὲ ἐσσεῖται τὸ περιεχόμενον ὑπὸ τῶν τᾶς ἑτέρας γραμμᾶς τμαμάτων τῷ τετραγώνῳ τῷ ἀπὸ τᾶς ἐπιψαυούσας τᾶς παραλλήλου αὐτᾷ. ἀποδέδεικται δὲ τοῦτο ἐν τοῖς κωνικοῖς στοιχείοις.

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Euclid, Fragmenta, ed. Heinrich Menge. 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/tlg1799.tlg016.local001/.