Old English secan "inquire, search for; pursue; long for, wish for, desire; look for, expect from," influenced by Old Norse soekja, both from Proto-Germanic *sakanan (source also of Old Saxon sokian, Old Frisian seka, Middle Dutch soekan, Old High German suohhan, German suchen, Gothic sokjan), from PIE *sag-yo-, from root *sag- "to track down, seek out" (source also of Latin sagire "to perceive quickly or keenly," sagus "presaging, predicting," Old Irish saigim "seek"). The natural modern form of the Anglo-Saxon word as uninfluenced by Norse is in beseech. Related: Sought; seeking.
1560s, "preponderance, dominance, leadership," originally of predominance of one city state or another in Greek history; from Greek hēgemonia "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 hēgemon "leader, an authority, commander, sovereign," from hēgeisthai "to lead," perhaps originally "to track down," from PIE *sag-eyo-, from root *sag- "to seek out, track down, trace" (see seek). In reference to modern situations from 1850, at first of Prussia in relation to other German states.
c. 1500, from French sagacité, from Latin sagacitatem (nominative sagacitas) "keenness of perception, quality of being acute," from sagax (genitive sagacis) "of quick perception, acute," related to sagus "prophetic," sagire "perceive keenly," from PIE root *sag- "to track down, trace, seek" (source also of Old English secan "to seek;" see seek). Also used 17c.-18c. of animals, meaning "acute sense of smell."
Much of the word's original meaning has been taken over by case (n.1), cause (n.), and it survives largely in phrases for the sake of (early 13c.) and for _______'s sake (c. 1300, originally for God's sake), both probably are from Norse, as these forms have not been found in Old English.