[1] Likewise in other lexica, beginning with Hesychius epsilon5327. Both the headword, a neuter noun, and the gloss, an abstract feminine one, come from the verb e)pitugxa/nw (epsilon 2738, epsilon 2674, cf. epsilon 3781) for 'hitting the right spot' and usually means a 'lucky find, something great stumbled on by chance'; cf. its synonyms at kappa 2772, kappa 2756. LSJ chooses to translate it here as 'natural advantages' but thus misses the colour of the metaphor.
[2] Diodorus Siculus 33.28b.3.1-5, on the arrival of Scipio Aemilianus and other Roman ambassadors in Egypt around 138 BC (an embassy that gave rise to a century of jockeying to be the general to reduce the country to a Roman province). The passage actually ends "grasped that a great empire could be established if this kingdom succeeded in finding (the verb e)/tuxon in the genitive absolute construction, cf. tau 1147) worthy leaders."