During that interval, Jupiter’s motion across the sky appears to slow. (Such erratic apparent motion stems from the complex combination of Earth’s own orbit around the sun with that of Jupiter.) A graph of Jupiter’s apparent velocity against time slopes downward, so that the area under the curve forms a trapezoid. The area of the trapezoid in turn gives the distance that Jupiter has moved along the ecliptic during the 60 days. Calculating the area under a curve to determine a numerical value is a basic operation, known as the integral between two points, in calculus. Discovering that the Babylonians understood this “was the real ‘aha!’ moment,” Ossendrijver says.
After cuneiform died out around 100 C.E., Babylonian astronomy was thought to have been virtually forgotten, he notes. It was left to French and English philosophers and mathematicians in the late Middle Ages to reinvent what the Babylonians had developed.