The Collaborative International Dictionary of English v.0.48:

Prevail \Pre*vail"\, v. i. [imp. & p. p. Prevailed; p. pr. &
   vb. n. Prevailing.] [F. pr['e]valoir, OF. prevaleir, L.
   praevalere; prae before + valere to be strong, able, or
   worth. See Valiant.]
   1. To overcome; to gain the victory or superiority; to gain
      the advantage; to have the upper hand, or the mastery; to
      succeed; -- sometimes with over or against.
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            When Moses held up his hand, Israel prevailed, and
            when he let down his hand, Amalek prevailed. --Ex.
                                                  xvii. 11.
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            So David prevailed over the Philistine. --1 Sam.
                                                  xvii. 50.
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            This kingdom could never prevail against the united
            power of England.                     --Swift.
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   2. To be in force; to have effect, power, or influence; to be
      predominant; to have currency or prevalence; to obtain;
      as, the practice prevails this day.
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            This custom makes the short-sighted bigots, and the
            warier skeptics, as far as it prevails. --Locke.
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   3. To persuade or induce; -- with on, upon, or with; as, I
      prevailedon him to wait.
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            He was prevailed with to restrain the Earl.
                                                  --Clarendon.
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            Prevail upon some judicious friend to be your
            constant hearer, and allow him the utmost freedom.
                                                  --Swift.
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The Collaborative International Dictionary of English v.0.48:

Prevailing \Pre*vail"ing\, a.
   1. Having superior force or influence; efficacious;
      persuasive. --Shak.
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            Saints shall assist thee with prevailing prayers.
                                                  --Rowe.
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   2. Predominant; prevalent; most general; as, the prevailing
      disease of a climate; a prevailing opinion.
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   Syn: Syn. See Prevalent.
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WordNet (r) 3.0 (2006):

prevailing
    adj 1: most frequent or common; "prevailing winds" [syn:
           prevailing, prevalent, predominant, dominant,
           rife]