The Collaborative International Dictionary of English v.0.48:

Curious \Cu"ri*ous\ (k?"r?-?s), a. [OF. curios, curius, F.
   curieux, L. curiosus careful, inquisitive, fr. cura care. See
   Cure.]
   1. Difficult to please or satisfy; solicitous to be correct;
      careful; scrupulous; nice; exact. [Obs.]
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            Little curious in her clothes.        --Fuller.
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            How shall we,
            If he be curious, work upon his faith? --Beau. & Fl.
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   2. Exhibiting care or nicety; artfully constructed;
      elaborate; wrought with elegance or skill.
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            To devise curious works.              --Ex. xxxv. 32
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            His body couched in a curious bed.    --Shak.
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   3. Careful or anxious to learn; eager for knowledge; given to
      research or inquiry; habitually inquisitive; prying; --
      sometimes with after or of.
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            It is a pity a gentleman so very curious after
            things that were elegant and beautiful should not
            have been as curious as to their origin, their uses,
            and their natural history.            --Woodward.
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   4. Exciting attention or inquiry; awakening surprise;
      inviting and rewarding inquisitiveness; not simple or
      plain; strange; rare. "Acurious tale" --Shak.
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            A multitude of curious analogies.     --Macaulay.
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            Many a quaint and curious volume of forgotten lore.
                                                  --E. A. Poe.
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            Abstruse investigations in recondite branches of
            learning or sciense often bring to light curious
            results.                              --C. J. Smith.
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   Curious arts, magic. [Obs.]
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            Many . . . which used curious arts brought their
            books together, and burned them.      --Acts xix.
                                                  19.

   Syn: Inquisitive; prying. See Inquisitive.
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Easton's 1897 Bible Dictionary:

Curious arts
   (Acts 19:19), magical arts; jugglery practised by the Ephesian
   conjurers. Ephesus was noted for its wizard and the "Ephesian
   spells;" i.e., charms or scraps of parchment written over with
   certain formula, which were worn as a safeguard against all
   manner of evils. The more important and powerful of these charms
   were written out in books which circulated among the exorcists,
   and were sold at a great price.