Both Uses

demonstrate
in
Dear John
(Edited)

Things were tense in the capitals of our NATO allies; on the news, there were demonstrations from the citizens and forceful proclamations from their leaders that the United States was about to make a terrible mistake.
Chpt 15 *

demonstrations = public protests
"All you have to do is grab near the hoof and tug while you tap the back of his leg here," she said, demonstrating.
Chpt 18 *

demonstrating = showing (how something is done)

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)