Regiment
late Middle English (in the sense ‘rule or government’): via Old French from late Latin regimentum ‘rule’, from regere ‘to rule’.
wiktionary
From Middle French regement, régiment, and its source, Late Latin regimentum(“direction for government; course of medical treatment”), from Latin regō(“rule”).
etymonline
regiment (n.)
late 14c., "government, rule, authority, control," a sense now obsolete, from Old French regiment "government, rule" (14c.), from Late Latin regimentum "rule, direction," from Latin regere "to rule, to direct, keep straight, guide" (from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule").
The military meaning "unit of an army" is recorded by 1570s, from a sense in French; the reference in the word originally was to permanent organization and discipline. The exact number of soldiers in a regiment has varied widely over time and place.
regiment (v.)
"to form into a regiment" with proper officers, hence "to organize, bring under a definite system of authority," 1610s, from regiment (n.). General sense of "organize systematically" is from 1690s. Related: Regimented; regimenting.