to talk out of both sides of ones mouth

from The Collaborative International Dictionary of English v.0.48
Mouth \Mouth\ (mouth), n.; pl. {Mouths} (mou[th]z). [OE. mouth,
   mu[thorn], AS. m[=u][eth]; akin to D. mond, OS. m[=u][eth],
   G. mund, Icel. mu[eth]r, munnr, Sw. mun, Dan. mund, Goth.
   mun[thorn]s, and possibly L. mentum chin; or cf. D. muil
   mouth, muzzle, G. maul, OHG. m[=u]la, Icel. m[=u]li, and Skr.
   mukha mouth.]
   1. The opening through which an animal receives food; the
      aperture between the jaws or between the lips; also, the
      cavity, containing the tongue and teeth, between the lips
      and the pharynx; the buccal cavity.
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   2. Hence: An opening affording entrance or exit; orifice;
      aperture; as:
      (a) The opening of a vessel by which it is filled or
          emptied, charged or discharged; as, the mouth of a jar
          or pitcher; the mouth of the lacteal vessels, etc.
      (b) The opening or entrance of any cavity, as a cave, pit,
          well, or den.
      (c) The opening of a piece of ordnance, through which it
          is discharged.
      (d) The opening through which the waters of a river or any
          stream are discharged.
      (e) The entrance into a harbor.
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   3. (Saddlery) The crosspiece of a bridle bit, which enters
      the mouth of an animal.
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   4. A principal speaker; one who utters the common opinion; a
      mouthpiece.
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            Every coffeehouse has some particular statesman
            belonging to it, who is the mouth of the street
            where he lives.                       --Addison.
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   5. Cry; voice. [Obs.] --Dryden.
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   6. Speech; language; testimony.
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            That in the mouth of two or three witnesses every
            word may be established.              --Matt. xviii.
                                                  16.
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   7. A wry face; a grimace; a mow.
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            Counterfeit sad looks,
            Make mouths upon me when I turn my back. --Shak.
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   {Down at the mouth} or {Down in the mouth}, chapfallen; of
      dejected countenance; depressed; discouraged. [Obs. or
      Colloq.]

   {Mouth friend}, one who professes friendship insincerely.
      --Shak.

   {Mouth glass}, a small mirror for inspecting the mouth or
      teeth.

   {Mouth honor}, honor given in words, but not felt. --Shak.

   {Mouth organ}. (Mus.)
      (a) Pan's pipes. See {Pandean}.
      (b) An harmonicon.

   {Mouth pipe}, an organ pipe with a lip or plate to cut the
      escaping air and make a sound.

   {To stop the mouth}, to silence or be silent; to put to
      shame; to confound.

   {To put one's foot in one's mouth}, to say something which
      causes one embarrassment.

   {To run off at the mouth}, to speak excessively.

   {To talk out of both sides of one's mouth}, to say things
      which are contradictory.
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            The mouth of them that speak lies shall be stopped.
                                                  --Ps. lxiii.
                                                  11.
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            Whose mouths must be stopped.         --Titus i. 11.
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