Theon Smyrnaeus De utilitate mathematicae 117

ed. Eduardus Hiller

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ἡ δὲ πεντὰς μέση ἐστι τῆς δεκάδος. ἐὰν γὰρ καθʼ ὁποιανοῦν σύνθεσιν ἐκ δύο ἀριθμῶν τὸν ι΄ συνθῇς,
μέσος εὑρεθήσεται ὁ ε΄ κατὰ τὴν ἀριθμητικὴν ἀναλο- γίαν· οἷον θ΄ καὶ α΄, καὶ η΄ καὶ β΄, καὶ ζ΄ καὶ γ΄, καὶ ϛ΄ καὶ δ΄· αἰεί τε ι΄ ποιήσεις καὶ μέσος εὑρεθήσεται ὁ ε΄ κατὰ τὴν ἀριθμητικὴν ἀναλογίαν, ὡς δηλοῖ τὸ διά- γραμμα, κατὰ πᾶσαν σύνθεσιν τῶν συμπληρούντων τὰ
ι΄ δυεῖν ἀριθμῶν [μέσος εὑρεθήσεται ὁ ε΄ κατὰ τὴν ἀριθμητικὴν ἀναλογίαν] τῷ ἴσῳ ἀριθμῷ τῶν ἄκρων ὑπερέχων τε καὶ ὑπερεχόμενος.

¹²

De utilitate mathematicae. Theon Smyrnaeus. ed. Eduardus Hiller. United States. 2016.

Funding provided by Harvard Library Arcadia Fund.

Current edition First1KGreek

De utilitate mathematicae (Greek) (Theon Smyrnaeus. Theonis Smyrnaei philosophi platonici Expositio rerum mathematicarum ad legendum Platonem utilium. Hiller, Eduard, editor. Leipzig: Teubner, 1878.)

Notes on the current edition

De utilitate mathematicae

1. 1 γ΄ om. apogr. τρὶς A 6 ἐλλήψεως A 9 οὕτω A

2. 10 post τῆ una lit. er. A. τετράδι; ι in ras. A 11 inscr περὶ τετράδος A, δ in mg. 13 καταυτὸ A. ἐδείχθη: cf. p. 58, 13. 87, 4 14 inscr. περὶ πεντάδος A, ε in mg. 15 τὸν Bull.] τῶν A 19 ὡς A2] ὧ A1

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Search the Perseus Catalog for:

Current edition First1KGreek

Notes on the current edition

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