Lewis & Short

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săgax, ācis, adj. [sagio; cf. salax, from salio], of quick perception, whose senses are acute, sagacious (class.).

  1. I. Lit.
    1. A. Chiefly of the acute sense of smelling in dogs, keen-scented: sagax Nasum habet, Plaut. Curc. 1, 2, 17: canes, Cic. Div. 1, 31, 65; Ov. M. 3, 207: catulus, id. R. Am. 201.
      With gen.: naris sagax, Luc. 7, 829.
      Poet.: virtus venandi, Ov. Hal. 76.
    2. B. Of other senses: sollicitive canes canibusve sagacior anser, Ov. M. 11, 599: palatum in gustu sagacissimum, Plin. 8, 37, 35, § 132.
  2. II. Trop., intellectually quick, keen, acute, shrewd, sagacious (syn.: sollers, perspicax, acutus, subtilis).
          1. (α) Absol.: (homo) animal hoc providum, sagax, multiplex, acutum, memor, plenum rationis et consilii, Cic. Leg. 1, 7, 22; cf. id. Fin. 2, 14, 45: mens, id. Tusc. 5, 23, 67; Lucr. 5, 420; 1, 1021: animus, id. 2, 840; 4, 913: ratio, id. 1, 131; 1, 369: homo sagax et astutus, Mart. 12, 87, 4: modo circumspectus et sagax, modo inconsultus ac praeceps, considerate, Suet. Claud. 15: mire sagaces fallere hospites, Hor. C. 2, 5, 22: curae, id. ib. 4, 4, 75.
            Of a soothsayer, knowing the future, Ov. M. 8, 316.
          2. (β) Ad aliquid (class.): ad suspicandum sagacissimus, Cic. Cat. 1, 8, 19: ad haec pericula perspicienda, Plancus ap. Cic. Fam. 10, 23, 4.
          3. (γ) With gen. (poet. and in post-Aug. prose): utilium sagax rerum et divina futuri, Hor. A. P. 218: fibrarum et pennae divinarumque flammarum, skilled in, Sil. 3, 344; cf. in sup.: prodigiorum (Joseph), Just. 36, 2, 8; and: rerum naturae, Col. praef., § 22 (with non ignarus).
          4. (δ) With in or simple abl. (post-Aug.): vir in conjecturis sagacissimus, Just. 1, 9, 14: civitas rimandis offensis sagax, Tac. H. 4, 11.
            (ρ) Inf.: sagax quondam ventura videre, Ov. M. 5, 146.
            Hence, adv.: să-gācĭter.
        1. a. Quickly, sharply, keenly, with quickness of scent, with a fine sense of smell: canes si advenientem sagaciter odorantur, Col. 7, 12, 7.
          Comp., Cic. Att. 6, 4, 3: vultures sagacius odorantur, Plin. 10, 69, 88, § 191; Hor. Epod. 12, 4.
          Sup., Cic. de Or. 2, 44, 186; Plin. 11, 37, 50, § 137.
        2. b. Trop., acutely, shrewdly, accurately, sagaciously: sagaciter pervestigare, Cic. de Or. 1, 51, 223: intueri, Quint. 2, 8, 4; Liv. 27, 28: perspicere naturam alicujus, Suet. Tib. 57 al.