Both Uses

demonstrate
in
Flags of Our Fathers
(Auto-generated)

The bloody battle of Tarawa had demonstrated the need for many more Marines trained to rout out well-entrenched Japanese defenders.†
Chpt 5. *
It was on March 4 that the lacerated, exhausted Marines saw the first demonstration of why they were fighting and dying on the ugly little island.†
Chpt 13.

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)