sagacity

1540–50; < Latin sagācitās wisdom, equivalent to sagāci- (stem of sagāx) wise (akin to seek) + -tās -ty²

Sagacity comes via Middle French sagacité, from Latin sagācitās (inflectional stem sagācitāt- ), whose original meaning was “keenness of scent, keenness of the senses in general, acuteness of mind, good judgment.” Sagācitās is a derivative of the adjective sagax (stem sagāc- ), which ultimately comes from the adjective sāgus “prophetic, prescient, practicing witchcraft” (Latin sāga means “witch, sorceress, wise woman”). English sagacity keeps the Latin and French meanings related to mental acuteness, but the meaning “keenness of scent” has been obsolete since the end of the 18th century.
Latin sāg- and sag- come from a Proto-Indo-European root sāg- (with variants) “to track by scent, track, seek out.” Sāg- becomes hēg- (dialect hāg- ) in Greek, forming the verb hēgeîsthai (dialect hāgeîsthai ) ”to guide”; Old Irish has saigim “I search.” The Germanic development of sāg- is sōk-, from which the verb sōkjan “to seek” is formed, becoming sēcan in Old English (English seek ).