The word demonstrate has a long history, and was already used in ancient Greece. This will be explained in a first part etymology before giving a more modern definition.
The etymology of Demonstrate
The word Demonstrate has etymologically two meanings:
1. To show concretely: “to present to visible perception” according to Plato.
2. To show by speech, to explain
The current definition of Demonstrate
Nowadays , Demonstrate has the meaning of establishing the truth of a proposition. It is necessary to arrive at a deduction by a sequence of necessary propositions.
Thus Nicolas Bourbaki explains,“The originality of the Greeks consists precisely in a conscious effort to arrange mathematical demonstrations in such a succession that the passage from one link to the next leaves no room for doubt and compels universal assent.”