# De utilitate mathematicae 87

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 87. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/87

ἀναλογία δʼ ἐστὶ πλειόνων λόγων ὁμοιότης ἢ ταὐτό- της, τουτέστιν ἐν πλείοσιν ὅροις λόγων ὁμοιότης, ὅταν ὃν ἔχει λόγον ὁ πρῶτος πρὸς τὸν δεύτερον, τοῦτον ὁ δεύτερος πρὸς τὸν τρίτον ἢ ἄλλος τις πρὸς ἄλλον. λέγεται δὲ ἡ μὲν συνεχὴς ἀναλογία, ἡ δὲ διῃρημένη, συνεχὴς μὲν ἡ ἐν ἐλαχίστοις τρισὶν ὅροις, διῃρημένη δὲ ἡ ἐν ἐλαχίστοις τέσσαρσιν. οἷον μετὰ τὴν ἐν ἴσοις ὅροις ἀναλογίαν συνεχὴς ἐν ἐλαχίστοις ὅροις κατὰ μὲν τὸ διαπλάσιον δʹ βʹ αʹ ἔστι γὰρ ὡς δʹ πρὸς β, οὕτως βʹ πρὸς ἕν. διρρημένη δὲ ϛʹ γ δʹ βʹ ἔστι γὰρ ὡς Ϛʹ πρὸς τὰ γ΄, οὕτως δʹ πρὸς τὰ β΄. τὸ δὲ αὐτὸ καὶ ἐπὶ τῶν ἄλλων πολλαπλασίων. ἔστι δὲ τρόπον τινὰ καὶ ἡ συνεχὴς ἐν τέτταρσιν ὅροις, δὶς λαμβανομένου τοῦ μέσου. καὶ ἐπὶ τῶν ἐπιμορίων δὲ ὁ αὐτὸς λόγος· συν- εχὴς μὲν ἀναλογία ἐν λόγῳ ἡμιολίῳ θʹ Ϛʹ δʹ, διῃρημένη δὲ θʹ Ϛʹ ιέ ί. ὁ δὲ αὐτὸς καὶ ἐπὶ τῶν ἄλλων λόγος.

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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/.