Etymology
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demonstrate (v.)

1550s, "to point out, indicate, exhibit," a sense now obsolete, from Latin demonstratus, past participle of demonstrare "to point out, indicate, demonstrate," figuratively, "to prove, establish," from de- "entirely" (see de-) + monstrare "to point out, show," from monstrum "divine omen, wonder" (see monster).

Meaning "to point out or establish the truth of by argument or deduction" is from 1570s. Sense of "describe and explain scientifically by specimens or experiment" is from 1680s. Meaning "take part in a public demonstration in the name of some political or social cause" is by 1888. Related: Demonstrated; demonstrating.

Latin also had commonstrare "point out, reveal," praemonstrare "show beforehand, foretell."

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Definitions of demonstrate

demonstrate (v.)
establish the validity of something, as by an example, explanation or experiment;
The experiment demonstrated the instability of the compound
Synonyms: prove / establish / show / shew
demonstrate (v.)
provide evidence for; stand as proof of; show by one's behavior, attitude, or external attributes;
This decision demonstrates his sense of fairness
Synonyms: attest / certify / manifest / evidence
demonstrate (v.)
march in protest; take part in a demonstration;
Thousands demonstrated against globalization during the meeting of the most powerful economic nations in Seattle
Synonyms: march
demonstrate (v.)
give an exhibition of to an interested audience;
Synonyms: show / demo / exhibit / present
From wordnet.princeton.edu