All 3 Uses of

demonstrate
in
Throne of Glass

She demonstrated for him, and her dagger found its mark.†
p. 108.7

demonstrated = showed

Dorian said, raising his brows as Celaena demonstrated a move for Nox.†
p. 204.9

She could scale a wall with ease, and had even demonstrated by climbing up to her own balcony with nothing but her bare hands.†
p. 327.2 *

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