# Scholia in Euclidis Data Ad prop. XCIV.

Scholia in Euclidem, Scholia in Euclidis Data, SCHOLIA.. Ancient Greek.

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

204. Πόθεν, ὅτι ἡ πρὸς ὀρθὰς αὐτῇ ἀγομένη ὡς ἐπὶ τὸ Ε πίπτει καὶ οὐκ ἐπὶ τὸ Η ἢ ἐνδοτέρω; καὶ σαφέστερον εἰπεῖν· κέντρου ὄντος τοῦ Η καὶ τῇ ΒΗ διαμέτρῳ πρὸς ὀρθὰς οὔσης τῆς ΝΗΞ, δεικτέον, ὅτι ἡ ἀπὸ τοῦ Α τῇ Α∠ πρὸς ὀρθὰς ἀγομένη οὔτε ἐπὶ τὸ Η πίπτει οὔτε ἐνδοτέρω τοῦ Η. ὅτι μὲν ἐκτὸς οὐ πεσεῖται τοῦ κύκλου, δῆλον· εἰ δὲ μή, ἐπʼ εὐθείας ἔσται τῇ Α∠· πιπτέτω δὲ ἐντὸς ὁπουδηποτοῦν τοῦ ἡμικυκλίου, ὡς ἐπὶ τὸ Κ· καὶ ἐπιζευχθεῖσα ἡ ΚΗ διήχθω ἐπὶ τὸ Θ ἢ ὁπου- δηποτοῦν. ἐπεζεύχθω δὲ καὶ ἡ ΑΘ· διάμετρός ἐστιν ἡ ΚΘ, ἡμικύκλιόν ἐστιν ἡ ΚΑΘ· ὀρθὴ ἄρα ἡ ὑπὸ ΚΑΘ· ἔστι δὲ καὶ ἡ ὑπὸ ∠ΑΚ ὀρθή· ἴσαι ἄρα ἀλ- λήλαις, ἡ μείζων τῇ ἐλάσ- σονι· ὅπερ ἐστὶν ἄτοπον. οὐκ ἄρα ἡ πρὸς ὀρθὰς ἀγο- μένη τῇ Α∠ ἐπὶ τὰ ἐντὸς τοῦ κύκλου ὡς ἐπὶ τὰ Κ, Α, Β πεσεῖται· ἐπʼ ἐκεῖνα ἄρα ὡς ἐπὶ τὸ Ε. 205. Ἡ ΘΑ διάμετρος p. 186, 4] πρὸς ὀρθὰς γὰρ ἦκται τῇ Α∠ ἡ ΑΕ, καὶ παράλληλος ἡ ΕΖ τῇ Α∠· αἱ ἄρα ὑπὸ ∠ΑΕ, ΑΕΖ δυσὶν ὀρθαῖς ἴσαι εἰσίν· ὥστε καὶ ἡ πρὸς τῷ Ε ὀρθή ἐστιν· ἐν ἡμικυκλίῳ ἄρα ἐστίν· διάμετρος ἄρα ἐστὶν ἡ ΑΘ. 206. P. 186, 7] οὕτως γὰρ κεῖται· καὶ τὸ ∠ δοθὲν καὶ ὁ κύκλος τῇ θέσει δεδομένος. 207. Ἴση ἄρα, φησίν, ὡς ἡ ΖΗ τῃ Η∠, καὶ ἡ ΘΖ τῇ Α∠· ἰσογώνια γὰρ τὰ Α∠Η, ΗΘΖ τρίγωνα· παραλλήλων γὰρ οὐσῶν τῶν Α∠, ΕΘ, αἱ ἐναλλὰξ γωνίαι αἱ ὑπὸ Α∠Η, ΗΖΘ ἴσαι εἰσίν. εἰσὶ δὲ διὰ τὸν αὐτὸν λόγον καὶ αἱ ὑπὸ ∠ΑΘ, ΑΘΖ ἴσαι ἀλλή- λαις· καὶ αἱ πρὸς τῷ Η κατὰ κορυφὴν οὖσαι ἴσαι εἰσίν· ἔστιν ἄρα, ὡς ἡ ΗΘ πρὸς ΗΑ, ἡ ΖΗ πρὸς Η∠. ἴση δὲ ἡ ΘΗ τῃ ΗΑ· ἴση ἄρα καὶ ἡ ΖΗ τῇ Η∠. ὁμοίως καὶ ἡ ΘΖ τῇ Α∠ ἴση ἐστίν. 208. Δοθὲν ἄρα ἐστί p. 186, 15] τὸ ὑπὸ τῶν ΕΖΘ δοθέν ἐστι διὰ τὸ 𝔮β΄.

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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/.