precinctyoudaoicibaDictYouDict
precinct: [15] The notion underlying precinct is of ‘encirclement’ or ‘enclosure’. It comes from the past participle of Latin praecingere ‘gird about, surround’. This was a compound verb formed from the prefix prae- ‘before, around’ and cingere ‘encircle with a belt’ (source of English cincture [16]). From the underlying notion come the twin modern meanings of an ‘area enclosed by walls’ and a ‘delimited district within a city’ (mainly used in American English).
=> cincture
liberty (n.)youdaoicibaDictYouDict
late 14c., "free choice, freedom to do as one chooses," from Old French liberté "freedom, liberty, free will" (14c.), from Latin libertatem (nominative libertas) "freedom, condition of a free man; absence of restraint; permission," from liber "free" (see liberal)
The spirit of liberty is the spirit which is not too sure it is right. [Learned Hand, 1944]
Nautical sense of "leave of absence" is from 1758. To take liberties "go beyond the bounds of propriety" is from 1620s. Sense of "privileges by grant" (14c.) led to sense of "a person's private land" (mid-15c.), which yielded sense in 18c. in both England and America of "a district within a county but having its own justice of the peace," and also "a district adjacent to a city and in some degree under its municipal jurisdiction" (as in Northern Liberties of Philadelphia). Also compare Old French libertés "local rights, laws, taxes."
parish (n.)youdaoicibaDictYouDict
c. 1300, "district with its own church; members of such a church," from Anglo-French paroche, parosse (late 11c.), Old French paroisse, from Late Latin parochia "a diocese," alteration of Late Greek paroikia "a diocese or parish," from paroikos "a sojourner" (in Christian writers), in classical Greek, "neighbor," from para- "near" (see para- (1)) + oikos "house" (see villa).

Sense development unclear, perhaps from "sojourner" as epithet of early Christians as spiritual sojourners in the material world. In early Church writing the word was used in a more general sense than Greek dioikesis, though by 13c. they were synonymous. Replaced Old English preostscyr, literally "priest-shire."