Both Uses of

demonstrate
in
Black: The Birth of Evil

A simple test will easily demonstrate whether or not I'm lying.†
Chpt 17 *

demonstrate = show

He managed them all, but never with the same precision she demonstrated.†
Chpt 22

demonstrated = showed

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