*peuk-

late 14c., "to decide, resolve; to arrange the time of (a meeting, etc.)," from Anglo-French appointer, Old French apointier "make ready, arrange, settle, place" (12c., Modern French appointer), from apointer "duly, fitly," from phrase à point "to the point," from a- "to" (see ad-) + point "point," from Latin punctum "small hole made by pricking" (from nasalized form of PIE root *peuk- "to prick").

The etymological sense is "to come to a point" (about some matter), therefore "agree, settle." The meaning "put in charge, authoritatively nominate or assign" is early 15c. Related: Appointed; appointing.

early 15c., appointement, "an agreement," also "a fixing of a date for official business," from Old French apointement, from apointer "arrange, settle, place" (see appoint). The meaning "act of placing in office" is attested from 1650s.