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Definition of sagacious : 1. Hence, of quick intellectual perceptions; of keen penetration and judgment; discerning and judicious; knowing; far- sighted; shrewd; sage; wise; as, a sagacious man; a sagacious remark.
2. Of quick sense perceptions; keen- scented; skilled in following a trail.

Synonyms:

subtile, clear-sighted, crafty, acute, cunning, witty, penetrative, commonsensible, penetrating, shrewd, balanced, politic, sensible, judicious, commonsensical, discriminating, well-founded, sage, sound, levelheaded, sapient, sane, rational, reasonable, keen, reason, subtle, clear-eyed, well-grounded, prudent

discerning, provident, forseeing, prescient, insightful, intuitive, second-sighted, prognostic, perceptive, prophetic, clairvoyant, farsighted, foresighted

expert, authoritative, scholarly, intellectual, philosophic, intelligent, brilliant, master, genius, adept, wise

cogent, gifted, brainy, profound, sharp, knowing, clever, erudite, sophisticated, bright, comprehending, knowledgeable, smart, capable, perspicacious, worldly, canny, astute, encyclopedic

Usage examples:

• Sagacious teachers and parents often blame and punish children for being what they made them. - "Dickens As an Educator", James L. (James Laughlin) Hughes.
• But it pleased a considerable portion of the public; and it so far satisfied Barbaja that the sagacious manager entrusted the young composer, now twenty years of age, with the libretto of Il Pirata, in which the principal part was to be written specially for Rubini. - "The Great Musicians: Rossini and His School", Henry Sutherland Edwards.
• Monsieur Pascal- the rational, sagacious Monsieur Pascal- was of opinion that she believed this herself. - "The Hour and the Man An Historical Romance", Harriet Martineau.