"military officer in ancient Rome," commander of a company of infantry, late 13c., from Latin centurionem (nominative centurio), "Roman army officer, head of a centuria" (a group of one hundred); see century. Latin centurio was glossed in Old English by hundredes ealdor.
1670s, "system of strict discipline," from the name of French military officer Jean Martinet (killed at the siege of Duisburg, 1672), lieutenant colonel in the Régiment du Roi, who in 1668 was appointed inspector general of the infantry. "It was his responsibility to introduce and enforce the drill and strict discipline of the French regiment of Guards across the whole infantry" [Olaf van Minwegen, "The Dutch Army and the Military Revolutions 1588-1688," 2006].
The meaning "an officer who is a stickler for discipline and regularity in small details" is first attested 1779 in English, but "No F[rench] use of the word in the sense of a disciplinarian appears" [Century Dictionary]. The surname is a diminutive of Latin Martinus (see Martin). Related: Martinetism.
1660s, "action of going the rounds" (of a military camp, etc.), from French patrouille "a night watch" (1530s), from patrouiller "go the rounds to watch or guard," originally "tramp through the mud," probably soldiers' slang, from Old French patouiller "paddle in water," which is probably from pate "paw, foot" (see patten). Compare paddlefoot, World War II U.S. Army slang for "infantry soldier." Meaning "those who go on a patrol" is from 1660s. Sense of "detachment of soldiers sent out to scout the countryside, the enemy, etc." is attested from 1702.
1640s, "small number of military men detailed for some purpose," from French esquade, from French escadre, from Spanish escuadra or Italian squadra "battalion," literally "square," from Vulgar Latin *exquadra "to square," from Latin ex "out" (see ex-) + quadrare "make square," from quadrus "a square" (from PIE root *kwetwer- "four"). Before the widespread use of of automatic weapons, infantry troops tended to fight in a square formation to repel cavalry or superior forces. Extended to sports 1902, police work 1905.