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Latin word exercitus comes from Latin arceo
arceo (Latin)
I defend, protect (from).. I keep off, ward off.. I shut up, enclose; box in.
exerceo (Latin)
I harass, worry. I keep busy, keep at work, drive on; occupy, employ, exercise (something in a form of action). I oversee, superintend, operate. I work (at).
exercitus (Latin)
(poetic) a multitude, host, swarm, flock. A troop, body of attendants. An exercised, disciplined body of men, an army. The assembly of the people in the Centuria Comitiata, as being a military organization. Trouble, affliction.