The Collaborative International Dictionary of English v.0.48:

Mediate \Me"di*ate\, v. i. [imp. & p. p. Mediated; p. pr. &
   vb. n. Mediating.] [LL. mediatus, p. p. of mediare to
   mediate. See Mediate, a.]
   [1913 Webster]
   1. To be in the middle, or between two; to intervene. [R.]
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   2. To interpose between parties, as the equal friend of each,
      esp. for the purpose of effecting a reconciliation or
      agreement; as, to mediate between nations.
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The Collaborative International Dictionary of English v.0.48:

Mediate \Me"di*ate\, v. t.
   1. To effect by mediation or interposition; to bring about as
      a mediator, instrument, or means; as, to mediate a peace.
      [1913 Webster]

   2. To divide into two equal parts. [R.] --Holder.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Mediate \Me"di*ate\, a. [L. mediatus, p. p. of mediare, v. t.,
   to halve, v. i., to be in the middle. See Mid, and cf.
   Moiety.]
   1. Being between the two extremes; middle; interposed;
      intervening; intermediate. --Prior.
      [1913 Webster]

   2. Acting by means, or by an intervening cause or instrument;
      not direct or immediate; acting or suffering through an
      intervening agent or condition.
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   3. Gained or effected by a medium or condition. --Bacon.
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            An act of mediate knowledge is complex. --Sir W.
                                                  Hamilton.
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WordNet (r) 3.0 (2006):

mediate
    adj 1: acting through or dependent on an intervening agency;
           "the disease spread by mediate as well as direct contact"
           [ant: immediate]
    2: being neither at the beginning nor at the end in a series;
       "adolescence is an awkward in-between age"; "in a mediate
       position"; "the middle point on a line" [syn: in-between,
       mediate, middle]
    v 1: act between parties with a view to reconciling differences;
         "He interceded in the family dispute"; "He mediated a
         settlement" [syn: intercede, mediate, intermediate,
         liaise, arbitrate]
    2: occupy an intermediate or middle position or form a
       connecting link or stage between two others; "mediate between
       the old and the new"