The Collaborative International Dictionary of English v.0.48:

Extremity \Ex*trem"i*ty\, n.; pl. Extremities. [L. extremitas:
   cf. F. extr['e]mit['e].]
   1. The extreme part; the utmost limit; the farthest or
      remotest point or part; as, the extremities of a country.
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            They sent fleets . . . to the extremities of
            Ethiopia.                             --Arbuthnot.
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   2. (Zo["o]l.) One of locomotive appendages of an animal; a
      limb; a leg or an arm of man.
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   3. The utmost point; highest degree; most aggravated or
      intense form. "The extremity of bodily pain." --Ray.
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   4. The highest degree of inconvenience, pain, or suffering;
      greatest need or peril; extreme need; necessity.
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            Divers evils and extremities that follow upon such a
            compulsion shall here be set in view. --Milton.
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            Upon mere extremity he summoned this last
            Parliament.                           --Milton.

   Syn: Verge; border; extreme; end; termination.
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WordNet (r) 3.0 (2006):

extremity
    n 1: an external body part that projects from the body; "it is
         important to keep the extremities warm" [syn: extremity,
         appendage, member]
    2: an extreme condition or state (especially of adversity or
       disease)
    3: the greatest or utmost degree; "the extremity of despair"
    4: the outermost or farthest region or point
    5: that part of a limb that is farthest from the torso