Tools

Greek Mathematics

Mathematical example.

(v.) Gnomons of Polygonal Numbers

Iambl. in Nicom. Arith. Introd., ed. Pistelli 62. 10–18

Καὶ ἐν τῇ σχηματογραφίᾳ δὲ τῶν πολυγώνων δύο μὲν ἐπὶ πάντων αἱ αὐταὶ μενοῦσι πλευραὶ μηκυνόμεναι καθ᾿ ἕκαστον, αἱ δὲ παρὰ ταύτας ἐναποληφθήσονται τῇ τῶν γνωμόνων περιθέσει αἰεὶ ἀλλασσόμεναι, μία μὲν ἐν τριγώνῳ, δύο δὲ ἐν τετραγώνῳ καὶ τρεῖς ἐν πενταγώνῳ καὶ ὁμοίως ἐπ᾿ ἄπειρον, κατὰ δυάδος κἀνταῦθα διαφορὰν τῆς κλήσεως τῶν πολυγώνων πρὸς τὴν ποσότητα τῶν ἀλλασσομένων γινομένης.

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Pythagorean Arithmetic

Mathematical example.

(v.) Gnomons of Polygonal Numbers

Iamblichus, On Nicomachus’s Introduction to Arithmetic, ed. Pistelli 62. 10–18

Now in the representation of the polygons two of the sides always remain the same but are produced, while the sides intercepted between them are continually changed when the gnomons are placed round, one being changed in the triangle, two in the square, three in the pentagon and so on to infinity, the difference between the designation of the polygons and the number of sides changed being two.a

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DOI: 10.4159/DLCL.pythagoras-arithmetic.1939