All 3 Uses of

demonstrate
in
The Lightning Thief

To reach his goal, he must first demonstrate great courage by succeeding as a keeper, finding a new camper and bringing him safely to Half-Blood Hill.†
Chpt 6

demonstrate = show

He told everybody he was going to demonstrate a disarming technique: how to twist the enemy's blade with the flat of your own sword so that he had no choice but to drop his weapon.†
Chpt 8 *

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