proper (adj.)

late 14c., "pertaining or belonging to oneself, not shared, peculiar to an individual only;" of a thing, "not open to the public, for the use of privileged persons;" of a religious rule, "not shared by Christians generally, distinctive;" from Latin privatus "set apart (from what is public), belonging to oneself (not to the state), peculiar, personal," used in contrast to publicus, communis.

This is a past-participle adjective from the verb privare "to bereave, deprive, rob, strip" of anything; "to free, release, deliver" from anything, from privus "one's own, individual," from Proto-Italic *prei-wo- "separate, individual," from PIE *prai-, *prei- "in front of, before," from root *per- (1) "forward." The semantic shift would be from "being in front" to "being separate."

Old English in this sense had syndrig. Of persons, "not holding public office or employment," recorded from early 15c. Of communications, "meant to be secret or confidential," 1550s. In private "privily" is from 1580s. Related: Privately.

Private school "school owned and run by individuals, not by the government, and run for profit" is by 1650s. Private parts "the pudenda" is from 1785 (privete "the sexual parts" is from late 14c.; secret parts in the same sense is from 16c.).

Private property "property of persons in their individual, personal, or private capacity," as distinguished from property of the state or public or for public use, is by 1680s. Private enterprise "business or commercial activity privately owned and free from direct state control" is recorded by 1797; private sector "part of an economy, industry, etc. that is free from state control" is from 1948.

Private eye "private detective, person engaged unofficially in obtaining secret information for or guarding the private interests of those who employ him" is recorded from 1938, American English (Chandler). Private detective "detective who is not a member of an official police force" is by 1856.

1775, French, "sensitive self-love, self-esteem;" see amour and proper.

Vanity usually gives the meaning as well, &, if as well, then better. [Fowler]

Middle English had it, translated, as proper love "self-love."