1560s, "to handle, train, or direct" (a horse), from the now-obsolete noun manage "the handling or training of a horse; horsemanship" (see manege, which is a modern revival of it), from Old French manège "horsemanship," from Italian maneggio, from maneggiare "to handle, touch," especially "to control a horse," which ultimately from Latin noun manus "hand" (from PIE root *man- (2) "hand").
Extended sense of "control or direct by administrative ability" any sort of business is by 1570s; meaning "to wield (a tool or object) by hand" is from 1580s. Meaning "effect by effort" (hence "succeed in accomplishing") is by 1732. Intransitive sense of "get by, carry on affairs" is suggested by 1650s, in frequent use from mid-19c. Related: Managed; managing. Managed economy was used by 1933.
Manage literally implies handling, and hence primarily belongs to smaller concerns, on which one may at all times keep his hand: as, to manage a house; to manage a theater. Its essential idea is that of constant attention to details: as, only a combination of great abilities with a genius for industry can manage the affairs of an empire. [Century Dictionary]
1580s, "one who directs or controls," agent noun from manage. Specific sense of "one charged with conducting a house of business or public institution" is from 1705.
1640s, "riding school, a school for training horses and teaching horsemanship;" by 1776, "the art of horsemanship, movements proper to a trained horse," from French manège, from Italian maneggio "the handling or training of a horse," from maneggiare "to control (a horse);" see manage (v.).
It forms all or part of: amanuensis; command; commando; commend; countermand; demand; Edmund; emancipate; legerdemain; maintain; manacle; manage; manciple; mandamus; mandate; manege; maneuver; manicure; manifest; manipulation; manner; manque; mansuetude; manual; manubrium; manufacture; manumission; manumit; manure; manuscript; mastiff; Maundy Thursday; mortmain; Raymond; recommend; remand; Sigismund.
It is the hypothetical source of/evidence for its existence is provided by: Hittite maniiahh- "to distribute, entrust;" Greek mane "hand," Latin manus "hand, strength, power over; armed force; handwriting," mandare "to order, commit to one's charge," literally "to give into one's hand;" Old Norse mund "hand," Old English mund "hand, protection, guardian," German Vormund "guardian;" Old Irish muin "protection, patronage."