Both Uses of

demonstrate
in
Harry Potter (#2) and the Chamber of Secrets

He tells me he knows a tiny little bit about dueling himself and has sportingly agreed to help me with a short demonstration before we begin.
p. 189.8 *

demonstration = display (showing how to do something)

Enough demonstrating! I'm going to come amongst you now and put you all into pairs.
p. 191.2

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