Sagacity, n.
Etymology: [L. sagacitas. See Sagacious.]
The quality of being sagacious; quickness or acuteness of sense perceptions; keenness of discernment or penetration with soundness of judgment; shrewdness. Some [brutes] show that nice sagacity of smell. Cowper. Natural sagacity improved by generous education. V. Knox.
Syn. -- Penetration; shrewdness; judiciousness. -- Sagacity, Penetration. Penetration enables us to enter into the depths of an abstruse subject, to detect motives, plans, etc. Sagacity adds to penetration a keen, practical judgment, which enables one to guard against the designs of others, and to turn everything to the best possible advantage.
Shades of meaning
Fernald has no entry of its own for sagacity; he lists it under acumen, wisdom.
Where he writes about it:
Sagacity is an uncultured skill in using quick perceptions for a desired end, generally in practical affairs; acumen may increase with study, and applies to the most erudite matters. — from acumen
Shrewdness is keenness or sagacity, often with a somewhat evil bias, as ready to take advantage of duller intellects. — from acumen
We speak of the acuteness of an observer or a reasoner, the insight and discernment of a student, a clergyman, or a merchant, the sagacity of a hound, the keenness of a debater, the shrewdness of a usurer, the penetration, perspicacity, and acumen of a philosopher. — from acumen
Insight, judgment, profundity or depth, reason, sagacity, sense, and understanding are native qualities of mind, tho capable of increase by cultivation. — from wisdom