late 14c., demonstratif, "characterized by logic, based on logic, showing or making manifest the truth or existence (of something)," from Old French démonstratif (14c.) and directly from Latin demonstrativus "pointing out, demonstrating," from demonstrat-, past-participle stem of demonstrare "to indicate, describe" (see demonstration).
The grammatical sense, "pointing out the thing referred to," is from mid-15c.; general sense of "having the quality of clearly showing, illustrative" is by 1520s. Meaning "given to or characterized by strong outward expressions of feelings" is from 1819. Related: Demonstratively; demonstrativeness.