The Collaborative International Dictionary of English v.0.48:

Dimidiate \Di*mid"i*ate\, a. [L. dimidiatus, p. p. of dimidiare
   to halve, fr. dimidius half. See Demi-.]
   1. Divided into two equal parts; reduced to half in shape or
      form.
      [1913 Webster]

   2. (Biol.)
      (a) Consisting of only one half of what the normal
          condition requires; having the appearance of lacking
          one half; as, a dimidiate leaf, which has only one
          side developed.
      (b) Having the organs of one side, or half, different in
          function from the corresponding organs on the other
          side; as, dimidiate hermaphroditism.
          [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Dimidiate \Di*mid"i*ate\, v. t. [imp. & p. p. Dimidiated; p.
   pr. & vb. n. Dimidiating.]
   1. To divide into two equal parts. [Obs.] --Cockeram.
      [1913 Webster]

   2. (Her.) To represent the half of; to halve.
      [1913 Webster]