To trench at

from The Collaborative International Dictionary of English v.0.48
Trench \Trench\, v. i.
   1. To encroach; to intrench.
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            Does it not seem as if for a creature to challenge
            to itself a boundless attribute, were to trench upon
            the prerogative of the divine nature? --I. Taylor.
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   2. To have direction; to aim or tend. [R.] --Bacon.
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   {To trench at}, to make trenches against; to approach by
      trenches, as a town in besieging it. [Obs.]
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            Like powerful armies, trenching at a town
            By slow and silent, but resistless, sap. --Young.
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