The differential and integral calculus, which Newton develops at the same time as the German Wilheim Leibniz (1646-1716), revolutionizes mathematics.
To know the area of a circle using the new tool, just divide that circle into even, small squares. Then the area of a square is calculated and multiplied by the total number of squares. This gives the area (or volume, if any) of any figure.
The squares must be infinitely small to fill the entire edge of the circle, and the number of squares must be infinite. So the total area will be a sum of infinite terms, the kind of sum the Greeks had known for over 2,000 years.