# Sectio canonis [Sp.] 8

Euclid, Sectio canonis [Sp.], Section 8. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/sectio-canonis-sp/8

Ἐὰν ἀπὸ ἡμιολίου διαστήματος ἐπίτριτον διάστημα ἀφαιρεθῇ, τὸ λοιπὸν καταλείπεται ἐπόγδοον. Ἔστω γὰρ ὁ μὲν α τοῦ β ἡμιόλιος, ὁ δὲ γ τοῦ β ἐπίτριτος. λέγω ὅτι ὁ α τοῦ ἐστὶν ἐπόγδοος. Ἐπεὶ γὰρ ὁ α τοῦ β ἐστὶν ἡμιόλιος, ὁ α ἄρα ἔχει τὸν β καὶ τὸ ἥμισυ αὐτοῦ. ὀκτὼ ἄρα οἱ α ἶσοί εἰσι δώδεκα τοῖς β. πάλιν ἐπεὶ ὁ τοῦ ἐστὶν ἐπίτριτος, ὁ γ ἄρα ἔχει θ Ϛ η τὸν β καὶ τὸ τρίτον αὐτοῦ. ἐννέα ἄρα οἱ γ ἶσοί εἰσι δώδεκα τοῖς β. δώδεκα δὲ οἱ β ἶσοί εἰσιν ὀκτὼ τοῖς α· ὀκτὼ ἄρα οἱ α ἶσοί εἰσιν ἐννέα τοῖς γ. ὁ α ἄρα ἶσός ἐστι τῷ γ καὶ τῷ ὀγδόῳ αὐτοῦ, ἄρα ὁ α τοῦ ἐστὶν ἐπόγδοος.

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Euclid, Sectio canonis [Sp.], ed. Karl von Jan. 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.tlg015.local002/.