 in ancient Greece were the prominent figures Udoxes of Nidus and Archimedes. They were able to prove areas of shapes through the method of exhaustion. For neural polygons, say an octagon, we split it up into a number of triangles and find the area of each triangle, then add it up to get the area of the polygon. Circles are a special case since they can't directly be split into triangles. Half a circle is just half a circle. So they inscribe to polygon and gradually increase the number of sides, so the area of the circle would approximately be equal to the area of the polygon. But the area of the circle would only be the same as the inscribed polygon with infinite sides. From this, we got the concept of limits, and it also incorporated the idea of the infinite process.