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sagacity (n.)

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."

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Definitions of sagacity from WordNet

sagacity (n.)
the mental ability to understand and discriminate between relations;
Synonyms: sagaciousness / judgment / judgement / discernment
sagacity (n.)
the trait of forming opinions by distinguishing and evaluating;
Synonyms: judiciousness / sagaciousness
From wordnet.princeton.edu