in Old English a common prefix with nouns, adjectives, adverbs, and verbs, "out, outward, outer; forth, away," from out (adv.). The use was even more common in Middle English, and also with the senses "outer, outside, on the outside, from without, external, externally; apart; greatly, extremely; completely, thoroughly, to completion." Other senses of out that extended into the use as a prefix include "beyond the surface or limits; to the utmost degree; to an explicit resolution."
In composition out has either its ordinary adverbial sense, as in outcast, outcome, outlook, etc., or a prepositional force, as in outdoors, or forms transitive verbs denoting a going beyond or surpassing of the object of the verb, in doing the act expressed by the word to which it is prefixed, as in outrun, outshine, outvenom, etc. In the last use especially out may be used with almost any noun or verb. [Century Dictionary]
1777, from maneuver (n.), or else from French manœuvrer "work, work with one's hands; carry out, prepare" (12c.), from Medieval Latin manuoperare. Originally in a military sense. Figurative use from 1801. Related: Maneuvered; maneuvering.
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Definitions of outmaneuver from WordNet
defeat by more skillful maneuvering;
The English troops outmaneuvered the Germans
My new supervisor knows how to outmaneuver the boss in most situations