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Old English fedan "nourish, feed, sustain, foster," from Proto-Germanic *fodjan (cf. Old Saxon fodjan, Old Frisian feda, Dutch voeden, Old High German fuotan, Old Norse foeða, Gothic fodjan "to feed"), from PIE *pa- "to protect, feed" (see food). Feeding frenzy is from 1989, metaphoric extension of a phrase that had been used of sharks since 1950s.
"action of feeding," 1570s, from feed (v.). Meaning "food for animals" is first attested 1580s. Of machinery, from 1892.
late 13c., from Old French fieu, fief "fief, possession, holding, domain; feudal duties, payment," from Medieval Latin feodum "land or other property whose use is granted in return for service," widely said to be from Frankish *fehu-od "payment-estate," or a similar Germanic compound, in which the first element is cognate with Old English feoh "money, movable property, cattle" (also German Vieh "cattle," Gothic faihu "money, fortune"), from PIE *peku- "cattle" (cf. Sanskrit pasu, Lithuanian pekus "cattle;" Latin pecu "cattle," pecunia "money, property"); second element similar to Old English ead "wealth."
OED rejects this, and suggests a simple adaptation of Germanic fehu, leaving the Medieval Latin -d- unexplained. Sense of "payment for services" first recorded late 14c. Fee-simple is "absolute ownership," as opposed to fee-tail "entailed ownership," inheritance limited to some particular class of heirs (second element from Old French taillir "to cut, to limit").