# De utilitate mathematicae 125

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 125. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/125

ὁ δὲ Ἐρατοσθένης φησὶν ὅτι πᾶς μὲν λόγος ἢ κατὰ διάστημα ἢ κατὰ τοὺς ὅρους αὔξεται· τῇ δὲ ἰσότητι συμ- βέβηκε διαστήματος μὴ μετέχειν· εὔδηλον δὲ ὅτι κατὰ τοὺς ὅρους μόνους αὐξηθήσεται. λαβόντες δὴ τρία με- γέθη καὶ τὴν ἐν τούτοις ἀναλογίαν κινήσομεν τοὺς ὅρους. καὶ δείξομεν ὅτι πάντα τὰ ἐν τοῖς μαθήμασιν ἐξ ἀναλογίας ποσῶν τινων σύγκειται καὶ ἔστιν αὐτῶν ἀρχὴ καὶ στοιχεῖον ἡ τῆς ἀναλογίας φύσις.

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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/.