There is a cluster of mathematical problems which at first sight seem quite disparate but which come together in a remarkable way. They have a history going back at least as far as Eudoxus and Archimedes, with their method of exhaustion. All of these problems come together in that branch of mathematics known as the calculus. The first step towards a grasp of the calculus is to understand what is meant by a graph. The calculus was invented, quite independently, by two men: the Englishman Sir Isaac Newton, arguably the greatest scientist of all time; and the brilliant German mathematician and philosopher G. W. Leibniz. Clearly the calculus bears on the paradoxes of the infinitely small. In order to see further bearing of the calculus on these paradoxes, it will be helpful to consider two more. They are modern embellishments of the earlier paradoxes. The first is due to Thomson, the second in essentials to J.A. Benardete.