Both Uses

demonstrate
in
The Watsons Go to Birmingham--1963
(Edited)

Today Miss Henry and I would like to give you a demonstration of your own possibilities in this regard.
p. 23.4 *

demonstration = display
Picketing, protest marches, and demonstrations made headlines.
p. 208.7 *

demonstrations = public protests or displays of support

Definitions:

(1) (demonstrate as in: It demonstrates my point.)
to show
The exact meaning of this sense of demonstrate can depend upon its context. For example:
- "I will demonstrate how to throw a Frisbee." -- show how to do something
- "I will demonstrate how much quicker the new computer is than the old one." -- show how something works
- "Her questioned demonstrated that she was listening and thinking deeply about what was said." -- showed to be true or proved
(2) (demonstrate as in: demonstrate to protest)
a public display supporting a cause -- usually joining with others in a political protest
(3) (meaning too rare to warrant focus)