Dictionary:

sagacity

  (sə-găs'ĭ-tē)

The quality of being discerning, sound in judgment, and farsighted; wisdom.

[French sagacité, from Old French sagacite, from Latin sagācitās, quickness of perception, from sagāx, sagāc-, of keen perception. See sagacious.]

Characteristics of intelligence, shrewdness, or wisdom; soundness of judgment.

noun

1. Skill in perceiving, discriminating, or judging: acumen, astuteness, clear-sightedness, discernment, discrimination, eye, keenness, nose, penetration, perceptiveness, percipience, percipiency, perspicacity, sageness, shrewdness, wit. See ability/inability, careful/careless.
2. Deep, thorough, or mature understanding: insight, profundity, sagaciousness, sageness, sapience, wisdom. See wise/foolish.

The noun has 2 meanings:

Meaning #1: ability to make good judgments
  Synonyms: sagaciousness, judgment, judgement, discernment

Meaning #2: the trait of forming opinions by distinguishing and evaluating
  Synonyms: judiciousness, sagaciousness