Etymology
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sag (v.)

late 14c., saggen, "hang down unevenly," also in Middle English "sink, be mired, sink down," possibly from a Scandinavian source related to Old Norse sokkva "to sink," or from Middle Low German sacken "to settle, sink" (as dregs in wine), from denasalized derivative of Proto-Germanic base *senkwanan "to sink" (see sink (v.)). A general North Sea Germanic word (compare Dutch zakken, Swedish sacka, Danish sakke). Of body parts by 1560s; of clothes by 1590s. Of other objects, "to droop, especially in the middle, as from weight or pressure" is by 1777. Related: Sagged; sagging.

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sag (n.)

"a bending or drooping," 1580s, in nautical use, "movement to leeward," from sag (v.). From 1727 in American English in reference to landforms having a sunken look. By 1861 in reference to droop from slackness in wires, cables, etc.

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saggy (adj.)

"apt to sag" [OED], 1848, from sag (n.) + -y (2). Related: Saggily; sagginess. Sagging (adj.) "that sags," present-participle adjective, is attested from 1590s.

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soke (n.)
"right of jurisdiction," Old English socn "jurisdiction, prosecution," literally "seeking," from Proto-Germanic *sokniz, from PIE *sag-ni-, from root *sag- "to seek out" (see seek). Related: Sokeman; sokemanry.
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sagacity (n.)

"state or character of being keenly perceptive; acuteness of mental discernment," 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. in reference to animals, with the meaning "acute sense of smell."

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exegesis (n.)
1610s, "explanatory note," from Greek exegesis "explanation, interpretation," from exegeisthai "explain, interpret," from ex "out" (see ex-) + hegeisthai "to lead, guide," from PIE root *sag- "to track down, seek out" (see seek (v.)). Meaning "exposition (of Scripture)" is from 1823. Related: Exegetic; exegetical; exegetically.
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hegemony (n.)

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.

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saw (n.1)

[toothed cutting tool] Middle English saue, from Old English sagu, from Proto-Germanic *sago "a cutting tool" (source also of Old English seax "knife," Old Norse sög, Norwegian sag, Danish sav, Swedish såg, Middle Dutch saghe, Dutch zaag, Old High German saga, German Säge "saw"), from PIE root *sek- "to cut" (source also of Latin secare "to cut").

In reference to its use as a musical instrument, by 1905. Saw-grass, the long, toothed grass found in the Southern U.S., is attested by 1822. The saw-fly (1773), destructive to plants, is so called for the construction of the insect's egg-depositing organ.

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seek (v.)

Middle English sēchen "go in search or quest of; strive for, try to attain," from Old English secan, seocan "search for; pursue, chase; long for, wish for, desire; look for, expect from," influenced by Old Norse soekja, both from Proto-Germanic *sokjanan (source also of Old Saxon sokian, Old Frisian seka, Middle Dutch soekan, Old High German suohhan, German suchen, Gothic sokjan).

This is reconstructed to be 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, had it not been influenced by Norse, is in beseech. Related: Sought; seeking. 

By late Old English as "ask a question." Seek-sorrow (1580s) was an old term for "a self-tormentor, one who contrives to vex himself." Seek-no-further (or farther) as the name of a type of eating apple is by 1660s.

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saga (n.)

1709, "ancient Scandinavian legend of considerable length," an antiquarians' revival to describe the medieval prose narratives of Iceland and Norway, from Old Norse saga "saga, story," cognate with Old English sagu "a saying" (see saw (n.2)).

Properly a long narrative composition of Iceland or Norway in the Middle Ages featuring heroic adventure and fantastic journeys, or one that has their characteristics. The extended meaning "long, convoluted story" is by 1857.

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