v. 1
To make stable or firm; to confirm.
v. 2
To form; to found; to institute; to set up in business.
v. 3
To appoint or adopt, as officers, laws, regulations, guidelines, etc.; to enact; to ordain.
v. 4
To prove and cause to be accepted as true; to demonstrate.

Related words

Word family: establisher establishment

Forms

Past participle: established
e.g. established → proved, demonstrated, ascertained, substantiated…

Choose the right word

Establish, Demonstrate or Prove?

To demonstrate is to force the mind to a conclusion by irresistible reasoning; to prove is rather to establish a fact by evidence; as, to prove one innocent or guilty.

J. C. Fernald, English Synonyms and Antonyms (1914)

Example sentences

prove Further study will prove that the theory is right.
demonstrate He went on to demonstrate how to use the machine.
ascertain We will first ascertain the cause of the disaster.
substantiate Sami won't be able to substantiate that alibi.
determine The doctors couldn't determine the cause of death.
locate The bat's sonar abilities allow it to locate prey.

Popularity over time

Word	1850 → 2019	Trend
establish		falling
prove		steady
demonstrate		rising
ascertain		falling
substantiate		falling
determine		falling

Use in printed books, per decade from 1850 to 2019.

By length

3 letters: set¹, fix¹, lay¹
4 letters: make¹, show¹, give¹, form¹, base¹, shew¹
5 letters: place¹, found¹, build¹, plant¹, prove¹, argue², erect², enact², forme
6 letters: ground¹, launch¹, secure², settle², verify³, locate², clinch¹, affirm², ratify³
7 letters: support², station², confirm², install², sustain², appoint²
8 letters: generate³, organize³, organise, sanction²
9 letters: institute³, determine³, prescribe², originate⁴, ascertain³
10 letters: constitute³, effectuate⁴
11 letters: demonstrate³, corroborate⁴
12 letters: substantiate⁴, authenticate⁴

The small number after each word is its number of syllables (argue² = 2 syllables).

In other languages

Français: affermir
Español: afirmar
Deutsch: festigen
Català: afermar