1560s , from Greek hegemonia  leadership , a leading the way , a going first ;  also  the authority or sovereignty of one city-state over a number of others ,  as Athens in Attica , Thebes in Boeotia ; from hegemon  leader ,  from hegeisthai  to lead ,  perhaps originally  to track down ,  from PIE * sag-eyo - , from root * sag -  to seek ...