Both Uses

demonstrate
in
The Thief, by Turner
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One arm was too tightly wrapped in bandages to move, but I held up the other to demonstrate that there was nothing up the sleeve of my nightshirt but my elbow.†
Chpt 12 *

demonstrate = show
This was no time to demonstrate unsuspected abilities.†
Chpt 3

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)