Both Uses

demonstrate
in
The Autobiography of Benjamin Franklin
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To promote that demand, I wrote and published a pamphlet, entitled "An Account of the new-invented Pennsylvania Fireplaces; wherein their Construction and Manner of Operation is particularly explained; their Advantages above every other Method of warming Rooms demonstrated; and all Objections that have been raised against the Use of them answered and obviated," etc. This pamphlet had a good effect.†
*

demonstrated = showed
Another thing demonstrated will be the propriety of everyman's waiting for his time for appearing upon the stage of the world.†

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)