The Collaborative International Dictionary of English v.0.48:

Supine \Su*pine"\ (s[-u]*p[imac]n"), a. [L. supinus, akin to sub
   under, super above. Cf. Sub-, Super-.]
   1. Lying on the back, or with the face upward; -- opposed to
      prone.
      [1913 Webster]

   2. Leaning backward, or inclining with exposure to the sun;
      sloping; inclined.
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            If the vine
            On rising ground be placed, or hills supine.
                                                  --Dryden.
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   3. Negligent; heedless; indolent; listless.
      [1913 Webster]

            He became pusillanimous and supine, and openly
            exposed to any temptation.            --Woodward.
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   Syn: Negligent; heedless; indolent; thoughtless; inattentive;
        listless; careless; drowsy.
        [1913 Webster] -- Su*pine"ly, adv. -- Su*pine"ness,
        n.
        [1913 Webster]

WordNet (r) 3.0 (2006):

supinely
    adv 1: with the face upward; "she was stretched supinely on her
           back"
    2: in an indifferently supine manner; "he called the tune to me
       and I supinely took it up"