The Collaborative International Dictionary of English v.0.48:

Assiduous \As*sid"u*ous\, a. [L. assiduus, fr. assid?re to sit
   near or close; ad + sed[=e]re to sit. See Sit.]
   1. Constant in application or attention; devoted; attentive;
      unremitting.
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            She grows more assiduous in her attendance.
                                                  --Addison.
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   2. Performed with constant diligence or attention;
      unremitting; persistent; as, assiduous labor.
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            To weary him with my assiduous cries. --Milton.
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   Syn: Diligent; attentive; sedulous; unwearied; unintermitted;
        persevering; laborious; indefatigable.
        [1913 Webster] As*sid"u*ous*ly, adv. --
        As*sid"u*ous*ness, n.
        [1913 Webster]

WordNet (r) 3.0 (2006):

assiduousness
    n 1: great and constant diligence and attention [syn:
         assiduity, assiduousness, concentration]