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.
1540s, "action of applying fire or setting on fire," verbal noun from fire (v.). From c. 1600 as "act of discharging firearms." Firing squad is attested from 1891 in reference to military executions; earlier as "those selected to fire over the grave of anyone interred with military honors" (1864); earlier in both senses is firing-party (1798 in reference to military executions; 1776 in reference to military funerals).
late 14c., "round, having the form of a circle," from Anglo-French circuler, Old French circuler "circular" (14c., Modern French circulaire), from Latin circularis, from circulus "small ring" (see circle (n.)). Meaning "intended for circulation" is from 1650s. The metaphoric circular firing squad is attested by 1990.
1560s, from Italian squadrone, augmentative of squadra "battalion," literally "square" (see squad). As a division of a fleet, from 1580s, of an air force, 1912.
1893, from French escadrille, from Spanish escuadrilla, diminutive of escuadra "square, squad, squadron," from Vulgar Latin *exquadrare, from Latin quadrare "to make square," related to quadrus "a square," quattuor "four" (from PIE root *kwetwer- "four").
also SWAT, 1968, acronym said to be for Special Weapons and Tactics squad or team; or Special Weapons Attack Team.
also linestock, lintstock, forked staff used for firing a cannon, 1570s, from Dutch lonstok, from lont "match" + stok "stick," from Proto-Germanic *stukkaz-, from PIE root *steu- (1) "to push, stick, knock, beat."