# Scholia in Euclidis Data Ad prop. LXVIII demonstr. alt.

Scholia in Euclidem, Scholia in Euclidis Data, APPENDIX SCHΟLIΟRUM.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/scholia-in-euclidem/scholia-in-euclidis-data/Ad%20prop.%20LXVIII%20demonstr.%20alt.

36. Πῶς δυνατὸν ποιῆσαι, ὡς τὸ Α παραλληλόγραμ- μον πρὸς τὸ Β παραλληλόγραμμον, οὕτως τὴν Κ πρὸς Λ; εἰλήφθω τῶν Γ∠, ΕΖ τρίτη ἀνάλογον. ἔστιν ἄρα ὡς ἡ πρώτη πρὸς τὴν τρίτην, οὕτως τὸ ἀπὸ τῆς πρώτης πρὸς τὸ ἀπὸ τῆς δευτέρας τὸ ὅμοιον καὶ ὁμοίως ἀνα- γραφόμενον, καὶ λοιπὸν ὡς ἐπὶ εὐθειῶν γεγονέτω, ὡς ἡ πρώτη πρὸς τὴν τρίτην, οὕτως ἡ Κ πρὸς Λ. 37. Τὸ Α ἄρα πρὸς τὸ Β p. 218, 3] ὡς δέδεικται ἐν τῷ ς΄ βιβλίῳ τοῦ Εὐκλείδου ἐν τῷ κγ΄ θεωρήματι. 38. Ἀλλὰ μὲν καὶ ἡ Κ p. 218, 6] ἐὰν ὦσι δύο εὐθεῖαι, καὶ ληφθῇ τις μία εὐθεῖα, ἡ μία τῶν πρότε- ρον πρὸς τὴν ἑτέραν λόγον ἔχει τὸν συγκείμενον ἔκ τε τοῦ ὃν ἔχει ἡ πρώτη πρὸς τὴν ἔξωθεν, ὡς ἔτυχεν, ληφθεῖσαν καὶ ὃν ἡ ληφθεῖσα πρὸς τὴν ἑτέραν. 39. Ὁ ἄρα συγκείμενος p. 218, 8] κεῖται δὲ ὡς τὸ Α πρὸς τὸ Β, οὕτως ἡ Κ πρὸς Λ· ὥστε καὶ ἡ Κ πρὸς Λ λόγον ἔχει τὸν συγκείμενον ἐκ τῶν πλευρῶν, τοῦ ὃν ἔχει ἡ Γ∠ πρὸς ΕΖ καὶ ἡ ΘΓ πρὸς ΕΗ.

---

Scholia in Euclidem, Scholia in Euclidis Data, 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/tlg5022.tlg002.local001/.