Both Uses of

demonstrate
in
The Witch of Blackbird Pond

Mercy demonstrated on two pieces of thin board to which were fastened strips of leather set with hooked wire teeth. From a great pile of heavy blue wool she pulled a small tuft, caught it in the wire teeth of one board, and drew across it the second board till the fibers were brushed flat.
p. 45.7 *

demonstrated = showed (how something is done)

Captain Talcott sensed the growing anger in the waiting crowd and raised his voice. "There is to be no demonstration," he reminded them.
p. 158.5 *

demonstration = public protest

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