To take to pieces; resolve into elements; separate, as a compound into its parts; ascertain the constituents or causes of; ascertain the characters or structure of, as a plant: as, to analyze a mineral, a sentence, or an argument; to analyze light by separating it into its prismatic constituents.Hence To examine critically, so as to bring out the essential elements or give the essence of: as, to analyze a poem.In mathematics, to submit (a problem) to treatment by algebra, and especially by the calculus.