Also Ambr. 1448. The two primary definitions are apparently extracted from a longer set; for the diverse meanings of the headword see LSJ, web address 1.
[1] This quotation (also at epsilon 3141) is from the end of Polybius’s account (15.9-16) of Hannibal’s defeat at Zama (OCD3 1633-34) in 202 BC by Scipio Africanus. The accidental event (ταὐτόματον ) is one that happens of its own accord (‘automatically’), i.e. outside any possible calculation. Polybius, in saying that no such event happened at Zama, implies that everything depended on the skill of the two successful generals in planning their tactics and implementing the plan; the better man won. This is designed as a compliment to his patron, Scipio Aemilianus.
[2] This proverb is the second line of an elegiac couplet, listed as of unknown authorship in Iambi et Elegi, ed. M.L. West, vol.2 (2nd. edn., Oxford,1992) §10. O.Crusius argued that the epigram is Hellenistic (Philologus 48, 1889, 1799), but later commentators compare it to the collection of epigrams attributed to Theognis (OCD3 1503): Bergk (Poetae Lyrici Graeci 3.690); Foulon and Weil (Polybius, Budé edn., vol.10, p.63n.), cf. West p.9. The use of ἀντέτυχεν is markedly similar to the same verb at [Theognis], El. 1.642, in a sequence where the end of a successful enterprise may not be what you wish, yet you cannot tell your true friends until you meet in your turn serious trouble; 2.1334, where, for using cruel words now, the boy sought may meet the same in his turn; cf. [Simonides], Epig. 7.516, where the poet prays that those who kill him should in their turn meet men like themselves. The uses of the compound exemplify well the root meaning of τυγχάνω ; cf. epsilon 3344 and its cross-references.
[3] The MSS read erroneously “Euchemus the Aegeatan”; see also epsilon 3821. Echemus (or Echemedon) of Tegea, the king of the Arcadians and a renowned wrestler (the winner at the legendary first Olympic Games, Pindar, Ol. 10.66 and scholia ad 79, 80), defeated Hyllus in single combat as the Heraclids first tried to enter the Peloponnese (Herodotus 9.26). See PW 5.1913; Hesiod, fr. 23a.31, 176.3 Merkelbach/West; Diodorus Siculus 4.58.3-5; etc. Pausanias saw the battle depicted on a stele at Tegea (8.53.10.8-10). We have no other evidence of the proverb being used of this fight, but he was the great hero of Tegea and it is appropriate there.