Precinct
late Middle English (denoting an administrative district): from medieval Latin praecinctum, neuter past participle (used as a noun) of praecingere ‘encircle’, from prae ‘before’ + cingere ‘gird’.
wiktionary
From Middle English precinct, precincte, early 15th century, in sense of “district for government purposes”, from Medieval Latin precinctum, alternative form of praecinctum(“enclosure, boundary line”), neuter singular of praecinctus, perfect passive participle of Latin praecingō(“surround, gird”), from prae(“before”) + cingō(“surround, encircle”), from which also cinch. [1]
Cognate to Italian precingere(“to encircle”).
etymonline
precinct (n.)
c. 1400, prasaynt (mid-15c. as precincte), "district defined for purposes of government or representation," especially in a city or town, from Medieval Latin precinctum "enclosure, boundary line," noun use of neuter past participle of Latin praecingere "to gird about, surround," from prae "before" (see pre-) + cingere "to surround, encircle" (see cinch (v.)). The meaning "exterior line or boundary encompassing a place" is from 1540s.