[1] For the several related applications of the headword machaira see LSJ s.v. The glossing word spa/qh likewise is attested in several senses, all related to the idea of a blade or something comparably shaped (cf. sigma ); the one required here is LSJ's no.6. (There is no need to invoke Lewis & Short, A Latin Dictionary s.v. spatha, III, 'a broad two-edged sword without a point (the Italian spada)'; this manifestly does not fit Appian's description of a pointed sword, about to be quoted here.)
[2] i.e. it can deliver an effective cut with both edges. The change of number from plural to singular ('swords . . . it has') is in the Greek.
[3] Polybius fr. 179 Büttner-Wobst [ = Polybius, Histories. Evelyn S. Shuckburgh, translator. London & New York (Macmillan) 1889; reprinted Bloomington 1962. fr.XXII (96), available on Perseus.] For the Celtiberians (and Polybius) see also under iota 112 = kappa 1306, and generally OCD(4) s.v. ('a name used by Graeco-Roman writers to describe several peoples (Arevaci, Lusones, etc.) living around the middle Ebro valley and in the eastern Meseta of Spain'). -- An alternative translation of e)pime/leia would be 'points in which they are so elaborately finished'. Büttner-Wobst notes (537-538) that Lipsius (Joest Lips, 1547-1606) attributed this fragment to Polybius. Büttner-Wobst also follows (ibid.) the suggestion by Lipsius that xeroi=n (hands, genitive dual of the feminine noun xei/r) be replaced by meroi=n (thus, from both parts); cf. n.2 above. As to the context, Walbank (754) notes that the fragment -- together with Polybius fr. 163; cf. iota 112 and n.2 thereto -- might belong either with the account of the Celtiberian War at Polybius 35.1 (web address 1) or with the geographical narrative at Polybius 34.8-9 (web address 2).
[4] See notes at beta 351 and theta 11. Like the 'solutions' quoted there, the words quoted here are in iambic trimeters.