sagacity (n.)

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.

late 14c., "something which portends or foreshadows," from Latin praesagium "a foreboding," from praesagire "to perceive beforehand, forebode," from praesagus (adj.) "perceiving beforehand, prophetic," from prae "before" (see pre-) + sagus "prophetic," related to sagire "perceive" (see sagacity).

c. 1600, "keenly perceptive, discerning," originally of persons in reference to the sense of smell," with -ous + stem of Latin sagax "of quick perception" (see sagacity). The sense of "skilled at discovering truths," especially as regards human natures, is by 1640s. It is not considered to be etymologically related to sage (adj.). Related: Sagaciously; sagaciousness.