# Synagoge 14

Pappus Alexandrinus, Synagoge, ΠΑΠΠΟΥ ΑΛΕΞΑΝΔΡΕΩΣ ΣΥΝΑΓΩΓΗ. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/14

14 κδ΄. Ἐπὶ δὲ τοῦ κε΄ θεωρήματος. Ἔστω τῶν μὲν Α Ε ἑκάτερος ἐλάσσων μὲν ἑκατοντάδος μετρούμενος δὲ ὑπὸ δεκάδος, ἕκαστος δὲ τῶν Γ ∠ Ε ἐλάσσων δεκάδος, καὶ δέον ἔστω τὸν ἐξ αὐτῶν στερεὸν εἰπεῖν. Ἔστωσαν γάρ τῶν Α Β πυθμένες οἱ Θ Κ, καὶ τῷ ἐκ τῶν Θ Κ Γ ∠ Ε στερεῷ ἴσος ἔστω ὁ Λ· ὅτι ὁ ἐκ τῶν Α Β Γ ∠ Ε στερεὸς ἴσος ἐστὶν ἑκατὸν τοῖς Λ. Ἔστι δὲ φανερὸν διὰ τῶν ἀριθμῶν, τοῦ Α ὄντος μονάδων κ΄ καὶ τοῦ Β μονάδων κ΄, καὶ τοῦ Γ μονάδων ε΄ καὶ τοῦ ∠ μονάδων Ϛ΄ καὶ τοῦ Ε μονάδων ζ΄, καὶ τῶν Θ Κ πυθμένων ὄντων μονάδων β΄· ὁ γὰρ ὑπὸ τῶν Θ Κ Γ ∠ Ε γίνεται στερεὸς μονάδων ωμ΄, οὗτος δὲ ἑκατοντάκις γενόμενος ἔσται μυριάδων η΄ μονάδων δ, ἴσος τῷ ἐκ τῶν Α Β Γ ∠ Ε στερεῷ ἀριθμῷ.

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Pappus Alexandrinus, Synagoge, ed. Friedrich Hultsch. 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/tlg2032.tlg001.local001/.