Look up the "epitaph of Stevinus" inscribed on his tombstone. It PROVES a point of physics about inclined planes and force.
There are some "proofs" of the pythagorean theorem which are little more than pictures, but you have to know what you are looking at.
What this article describes is nothing of the sort.
There is no such thing as proof by picture.
You contradict yourself. The pythagorean "picture" that you bring up suffices to prove the theorum.
The crap that high school teachers dish out about the scientific method has little to do with real science alas. Many times a thought experiment works better to settle a question than observation or measurement.
You cannot prove anything in physics. What you can prove are results about the mathematical model. People often get confused about that point. To see this, please observe that "normal force" isn't a force at all, but an accounting gimmick.
Look up
If you want to make a point, make it, I'm not going to do your work for you.