# De utilitate mathematicae 180

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 180. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/180

πῶς οὖν σώσει τὰ φαινόμενα; ἔστω κέντρον τοῦ ἡλιακοῦ κύκλου τὸ μ, καὶ γεγράφθω κέντρῳ μὲν τῷ θ, διαστήματι δὲ τῷ θμ, κύκλος ὁ μονξ, καὶ ὑποκείσθω ὁ εξηκ κύκλος νῦν συναποφέρεσθαι μὲν τῷ παντὶ τὴν ἀπὸ τῶν ἀνατολῶν ἐπὶ δύσεις φοράν, ἤτοι δὲ διὰ βραδυτῆτα ὑπολειπόμενος, ἢ καὶ φερόμενος ὑπεναντίως τῷ παντί, ὃ καὶ μᾶλλον δοκεῖ τῷ Πλάτωνι, ὥστε τὸ μὲν κέντρον κατὰ τοῦ μονξ κύκλου φερόμενον ὁμαλῶς περιπορεύε- σθαι αὐτὸν ἐνιαυτῷ, καὶ ἐν τῷ 〈αὐτῷ〉 χρόνῳ τὸν ἥλιον διανύειν τὸν ἑαυτοῦ κύκλον, ὁμοίως φερόμενον ὁμαλῶς. πάλιν ὁ ἥλιος κατὰ τοῦ εζηκ κύκλου ἤτοι ἐπὶ τὰ αὐτὰ τῷ παντὶ ἐνεχθήσεται, ἢ ὑπεναντίως, 〈ἐπὶ τὰ αὐτὰ δὲ〉 τῷ ἰδίῳ κύκλῳ, οἷον ἀπὸ τοῦ κ ἐπὶ τὸ ε καὶ ἀπὸ τοῦ ε ἐπὶ τὸ ζ. λέγω δὲ ὅτι τοῦ εζηκ κύκλου περιφερομένου κατὰ τοῦ μονξ ὑπεναντίως τῷ παντὶ ὁ ἥλιος ἐπὶ τοῦ εζηκ κύκλου ἐνεχθήσεται ἐπὶ τὰ αὐτὰ τῷ παντὶ καὶ σώσει τὰ φαινόμενα.

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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/.