quart (n.)

liquid measure of capacity equal to one-fourth of a gallon, early 14c., from Old French quarte "a fourth part" (13c.), from Latin quarta (pars), fem. of quartus "the fourth, fourth part" (related to quattuor "four," from PIE root *kwetwer- "four").

Compare Latin quartarius "fourth part," also the name of a small liquid measure (the fourth part of a sextarius), which was about the same as an English pint.