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late 13c., "strenuous, ardent, fierce, angry," from Old French aigre "sour, acid; harsh, bitter, rough; eager greedy; lively, active, forceful," from Latin acrem (nominative acer) "keen, sharp, pointed, piercing; acute, ardent, zealous" (see acrid).
Meaning "full of keen desire" (early 14c.) seems to be peculiar to English. The English word kept an alternative meaning of "pungent, sharp-edged" till 19c. (e.g. Shakespeare's "The bitter clamour of two eager tongues," in "Richard II"). Related: Eagerly; eagerness.