The Collaborative International Dictionary of English v.0.48:

Medium \Me"di*um\, n.; pl. L. Media, E. Mediums. [L.
   medium the middle, fr. medius middle. See Mid, and cf.
   Medius.]
   1. That which lies in the middle, or between other things;
      intervening body or quantity. Hence, specifically:
      (a) Middle place or degree; mean.
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                The just medium . . . lies between pride and
                abjection.                        --L'Estrange.
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      (b) (Math.) See Mean.
      (c) (Logic) The mean or middle term of a syllogism; that
          by which the extremes are brought into connection.
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   2. A substance through which an effect is transmitted from
      one thing to another; as, air is the common medium of
      sound. Hence: The condition upon which any event or action
      occurs; necessary means of motion or action; that through
      or by which anything is accomplished, conveyed, or carried
      on; specifically, in animal magnetism, spiritualism, etc.,
      a person through whom the action of another being is said
      to be manifested and transmitted.
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            Whether any other liquors, being made mediums, cause
            a diversity of sound from water, it may be tried.
                                                  --Bacon.
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            I must bring together
            All these extremes; and must remove all mediums.
                                                  --Denham.
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   3. An average. [R.]
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            A medium of six years of war, and six years of
            peace.                                --Burke.
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   4. A trade name for printing and writing paper of certain
      sizes. See Paper.
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   5. (Paint.) The liquid vehicle with which dry colors are
      ground and prepared for application.
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   6. (Microbiology) A source of nutrients in which a
      microorganism is placed to permit its growth, cause it to
      produce substances, or observe its activity under defined
      conditions; also called culture medium or growth
      medium. The medium is usually a solution of nutrients in
      water, or a similar solution solidified with gelatin or
      agar.
      [PJC]

   7. A means of transmission of news, advertising, or other
      messages from an information source to the public, also
      called a news medium, such as a newspaper or radio; used
      mostly in the plural form, i. e. news media or media.
      See 1st media[2].
      [PJC]

   Circulating medium, a current medium of exchange, whether
      coin, bank notes, or government notes.

   Ethereal medium (Physics), the ether.

   Medium of exchange, that which is used for effecting an
      exchange of commodities -- money or current
      representatives of money.
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