# Sphaerica 22.ΠΡΟΤΑΣΙΣ κβ′. ΘΕΩΡ. b

Theodosius of Bithynia, Sphaerica, ΒΙΒΛΙΟΝ ΠΡΩΤΟΝ., Chapter 22. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theodosius-of-bithynia/sphaerica/22.%CE%A0%CE%A1%CE%9F%CE%A4%CE%91%CE%A3%CE%99%CE%A3%20%CE%BA%CE%B2%E2%80%B2.%20%CE%98%CE%95%CE%A9%CE%A1.%20b

Ἐὰν ἐν σφαίρᾳ εὐθεῖά τις διὰ τοῦ κέντρου οὖσα εὐθεῖάν τινα μὴ διὰ τοῦ κέντρου οὖσαν δίχα τέμνῃ, καὶ πρὸς ὀρθὰς αὐτὴν τεμεῖ· καὶ ἐὰν πρὸς ὀρθὰς αὐτὴν τέμνῃ, καὶ δίχα αὐτὴν τεμεῖ. Ἡ ἀπόδειξις, ὡς ἐν τοῖς κυκλικοῖς. Ἐὰν γὰρ διὰ τῆς διαμέτρου διὰ τοῦ κέντρου οὔσης τῆς σφαίρας, καὶ τῆς μὴ· διὰ τοῦ κέντρου οὔσης ἐπίπεδον ἐκβληθῇ, τομὴν ποιήσουσι γραμμὴν κύκλον· καὶ ἔσται ἐν κύκλῳ εὐθεῖά τις διὰ τοῦ κέντρου οὖσα εὐθεῖάν τινα μὴ διὰ τοῦ κέντρου οὖσαν δίχα τέμνουσα, ὥστε καὶ πρὸς ὀρθὰς αὐτὴν τεμεῖ· καὶ ἐὰν πρὸς ὀρθὰς αὐτὴν τέμνῃ, καὶ δίχα αὐτὴν τεμεῖ.

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Theodosius of Bithynia, Sphaerica, ed. Ernst Nizze. 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/tlg1719.tlg001.local001/.