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A solution of the old geometrical problem of dividing a given length into extreme and mean ratio. In this division, the ratio of the short to the long segment equals the ratio of the long to the whole segment. This can be stated in even more general terms for any two identifiable and separate quantities (of length, time, number, amount, etc.): the lesser is to the greater as the greater is to the sum (Michael Rogers, "Rehearings: Chopin, Prelude in A Minor, op. 28, no. 2," 19th Century Music 4 (Spring 1981): 246)