The Collaborative International Dictionary of English v.0.48:

Heave \Heave\ (h[=e]v), v. i.
   1. To be thrown up or raised; to rise upward, as a tower or
      mound.
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            And the huge columns heave into the sky. --Pope.
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            Where heaves the turf in many a moldering heap.
                                                  --Gray.
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            The heaving sods of Bunker Hill.      --E. Everett.
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   2. To rise and fall with alternate motions, as the lungs in
      heavy breathing, as waves in a heavy sea, as ships on the
      billows, as the earth when broken up by frost, etc.; to
      swell; to dilate; to expand; to distend; hence, to labor;
      to struggle.
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            Frequent for breath his panting bosom heaves.
                                                  --Prior.
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            The heaving plain of ocean.           --Byron.
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   3. To make an effort to raise, throw, or move anything; to
      strain to do something difficult.
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            The Church of England had struggled and heaved at a
            reformation ever since Wyclif's days. --Atterbury.
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   4. To make an effort to vomit; to retch; to vomit.
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   To heave at.
      (a) To make an effort at.
      (b) To attack, to oppose. [Obs.] --Fuller.

   To heave in sight (as a ship at sea), to come in sight; to
      appear.

   To heave up, to vomit. [Low]
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