Quart

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Middle English: from Old French quarte, from Latin quarta (pars) ‘fourth (part)’, from quartus ‘fourth’, from quattuor ‘four’.

wiktionary

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From French quart, from Latin quartus(“one-fourth”). Cognate with Spanish cuarto(“quarter; room, quarters”).

etymonline

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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.