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1650s, "a begining with the same letter," from Modern Latin alliterationem (nominative alliteratio), noun of action from past participle stem of alliterare "to begin with the same letter," from Latin ad- "to" (see ad-) + littera (also litera) "letter, script" (see letter). Formed on model of obliteration, etc. Related: Alliterational.
The repetition of the beginning sounds of words, as in “Peter Piper picked a peck of pickled peppers,” “long-lived,” “short shrift,” and “the fickle finger of fate.”