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From: Webster's Revised Unabridged Dictionary (1913)

 Re·cip·ro·cal·ly adv.
 1. In a reciprocal manner; so that each affects the other, and is equally affected by it; interchangeably; mutually.
    These two particles do reciprocally affect each other with the same force.   --Bentley.
 2. Math. In the manner of reciprocals.
 Reciprocally proportional Arith. & Alg., proportional, as two variable quantities, so that the one shall have a constant ratio to the reciprocal of the other.