The Collaborative International Dictionary of English v.0.48:

Sagacious \Sa*ga"cious\, a. [L. sagax, sagacis, akin to sagire
   to perceive quickly or keenly, and probably to E. seek. See
   Seek, and cf. Presage.]
   1. Of quick sense perceptions; keen-scented; skilled in
      following a trail.
      [1913 Webster]

            Sagacious of his quarry from so far.  --Milton.
      [1913 Webster]

   2. 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.
      [1913 Webster]

            Instinct . . . makes them, many times, sagacious
            above our apprehension.               --Dr. H. More.
      [1913 Webster]

            Only sagacious heads light on these observations,
            and reduce them into general propositions. --Locke.
      [1913 Webster]

   Syn: See Shrewd.
        [1913 Webster] -- Sa*ga"cious*ly, adv. --
        Sa*ga"cious*ness, n.
        [1913 Webster]

WordNet (r) 3.0 (2006):

sagaciousness
    n 1: the mental ability to understand and discriminate between
         relations [syn: sagacity, sagaciousness, judgment,
         judgement, discernment]
    2: the trait of forming opinions by distinguishing and
       evaluating [syn: judiciousness, sagacity,
       sagaciousness]