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.]
      [1913 Webster]

   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.
      [1913 Webster]

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.
      [1913 Webster]

   3. Gained or effected by a medium or condition. --Bacon.
      [1913 Webster]

            An act of mediate knowledge is complex. --Sir W.
                                                  Hamilton.
      [1913 Webster]

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"

Moby Thesaurus II by Grady Ward, 1.0:

49 Moby Thesaurus words for "mediate":
   accommodate, act between, act for, adjust, advance, arbitrate,
   arrange matters, assist, bargain, be instrumental, bring to terms,
   bring together, compose, compromise, facilitate, fix up, forward,
   go between, harmonize, heal the breach, intercede, interfere,
   intermediate, interpose, intervene, judge, make terms,
   meet halfway, minister to, moderate, negotiate, patch things up,
   promote, put in tune, reconcile, referee, represent, resolve,
   restore harmony, reunite, serve, settle, settle differences,
   smooth it over, step in, subserve, treat with, umpire,
   weave peace between



Bouvier's Law Dictionary, Revised 6th Ed (1856):

MEDIATE, POWERS. Those incident to primary powers, given by a principal to
his agent. For example, the general authority given to collect, receive and
pay debts due by or to the principal is a primary power. In order to
accomplish this it is frequently required to settle accounts, adjust
disputed claims, resist those which are unjust, and answer and defend suits;
these subordinate powers are sometimes called mediate powers. Story, Ag.
Sec. 58. See Primary powers, and 1 Camp. R. 43, note 4 Camp. R. 163; 6 S. &
R. 149.