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redound (v.)

late 14c., redounden, "to overflow, flow abundantly; abound, multiply, increase" (senses now obsolete), also "to flow or go back" (to a place or person), "be sent, rolled, or driven back," from Old French redonder "overflow, abound, be in profusion" (12c.), from Latin redundare "to overflow" (see redundant). Hence "to contribute, have effect" (to the credit, honor, etc.), early 15c. Related: Redounded; redounding.

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Definitions of redound from WordNet

redound (v.)
return or recoil;
Fame redounds to the heroes
redound (v.)
contribute;
Everything redounded to his glory
redound (v.)
have an effect for good or ill;
Her efforts will redound to the general good
From wordnet.princeton.edu