Perspicacity, n.
Etymology: [L. perspicacitas: cf. F. perspicacité. See Perspicacious.]
The state of being perspicacious; acuteness of sight or of intelligence; acute discernment. Sir T. Browne.
Shades of meaning
Fernald has no entry of its own for perspicacity; he lists it under acumen.
Where he writes about it:
Insight and discernment are applied oftenest to the judgment of character; penetration and perspicacity to other subjects of knowledge. — from acumen
Perspicacity is the power to see clearly through that which is difficult or involved. — 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