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Old English *fostrian "to supply with food, nourish, support," from fostor "food, nourishment, bringing up," from Proto-Germanic *fostrom, from root *foth-/*fod- (see food).
Meaning "to bring up a child with parental care" is from c.1200; that of "to encourage or help grow" is early 13c. of things; 1560s of feelings, ideas, etc. Old English also had the adjective meaning "in the same family but not related," in fostorfæder, etc. Related: Fostered; fostering.