How did Green's Theorem emerged?

Question

I was looking how Green's theorem is used and I only found that is to compute line integrals, that are too hard, in form of a double integral. I initially thought that Green's theorem had a physical interpretation, then reading a book about vectorial calculus it mentioned that Green's theorem can be looked at in the same way as the fundamental theorem of calculus. This really didn't cleared my doubts, How did Green's Theorem emerged? By this I mean, why was it formulated? What problem was trying to be solved that Green's Theorem had to be stated?, From what preliminary ideas did it emerged? I believe there should be an intuitive way to understand Green's theorem, like I did with calculus, I learned about squearing circles and finding the instant velocity, then it made sense, I understood why and how calculus emerged, what was it trying to solve, and I think it is similar to this situation. Where did it come from? Did it just popped into existence and it worked? That's how books try to present it, at least that appears to me, there's no background.