# De utilitate mathematicae 206

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 206. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/206

ἐπεὶ τοίνυν ἐπʼ εὐθείας τῶν φωτιζόντων αἱ ἀκτῖνες καὶ αἱ αὐγαὶ πίπτουσι καὶ παραπλησίως συνεχεῖς ταύ- ταις αἱ σκιαί, ὅταν μὲν ἴσον τό τε φωτίζον καὶ τὸ τὴν σκιὰν ἀποβάλλον, σφαιρικὰ δὲ ἄμφω, γίνεται ἡ [δὲ] σκιὰ κυλινδρικὴ καὶ εἰς ἄπειρον ἐκπίπτουσα. οἷον ἔστω φωτίζον μὲν τὸ αβ, φωτιζόμενον δὲ τὸ γδ, ἴσα δὲ ἀλλήλοις καὶ σφαιρικά· δῆλον οὖν ὡς τῆς γε αγ ἀκτῖνος καὶ τῆς βδ ἐπʼ εὐθείας ἐκπιπτουσῶν, ἐπεὶ αἱ αβ γδ διάμετροι ἴσαι τέ εἰσιν ἀλλήλαις καὶ πρὸς ὀρθὰς ταῖς ἄγ βδζ ἐφαπτομέναις, παράλληλοι ἔσονται, καὶ αἱ γε δζ ἐπʼ ἄπειρον ἐκβαλλόμεναι οὐ συμπεσοῦνται· τοῦ δὲ τοιούτου πάντοθεν γινομένου δῆλον ὡς τῆς γδ σφαί- ρας ἡ σκιὰ κυλινδρικὴ τε ἔσται καὶ ἐπʼ ἄπειρον ἐκπί- πτουσα.

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Theon Smyrnaeus, De utilitate mathematicae, ed. Eduardus Hiller. 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/tlg1724.tlg001.local001/.