Both Uses

demonstrate
in
The Boy on the Wooden Box
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When I think of all his many actions as a rescuer, big and small, it is this one act that first comes to mind; I think perhaps because it demonstrates such extraordinary compassion.†
p. 147.6 *

demonstrates = shows
Nazi propaganda portrayed the events of that night as a spontaneous demonstration against Jews as retaliation for the killing of a German diplomat in Paris by a young Jew named Herschel Grynszpan.†
p. 42.6

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)