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The idea about approximating a circles circumference/area with inscribed and described perfect polygons is also from calculus, but was first used in ancient Greece.
What a coincidence... I am doing a project on exactly this (Newton vs Leibniz)!
Historically, it is agreed that both get the credit. Newton seems to have discovered it prior to Leibniz but did not publish. Less well known, is that earlier mathematicians like Fermat were discovering portions of it. Even Johannes Kepler solved an integration by stuffing rectangles under a curve and imagining what would happen if there were an infinite number of rectangles that were infinitely small. The beginnings of integral calculus.
I have a question about limits. I am taking a University course at Yale on Vectors and Calculus and I consider my self to be very well versed at limits, derivatives etc. However, I still have one question. Who created Calculus? We are all aware of Newton being the main "creator". But what about Gottfried Wilhelm Leibniz?