Left: Cuneiform tablet, with calculations that involved a trapezoid.
Right: The distance travelled by Jupiter after 60 days, 10º45′, is computed as the area of the trapezoid. The trapezoid is then divided into two smaller ones in order to find the time (tc) in which Jupiter covers half this distance.
The Ancient Babylonians could predict the passage of Jupiter through the night sky, which they recorded on cuneiform tablets – more than 14 centuries before such techniques were seen in Europe.
The discovery was made by Mathieu Ossendrijver of Humboldt University in Berlin, who studied five cuneiform tablets that date to between 350 and 50 BC, recovered during 19th-century excavations near the main temple Esagila in Babylon, and now held by the British Museum in London.
They record calculations for the time and velocity of the planet’s journey over 60 days. Four describe an area covered over a certain period of time as a trapezoid, but the figures could not be connected to a named planet. However, when Ossendrijver examined the fifth, previously unstudied, tablet, he noticed it specifically mentions Jupiter – and that the figures match those on the other four tablets.
Though contemporary Greeks and Egyptians had mastered astronomy, this particular geometrical method is new, as Ossendrijerexplained: ‘The motion of a planet from day to day is generally computed from its velocity (which is the distance covered per day) but, uniquely on these tablets, the total distance covered in a certain period of time (60 days) is computed from the area under the trapezoid figure obtained by drawing velocity against time.’
This approach will appear strikingly familiar to students of physics and mathematics today, as it anticipates modern integral calculus that can be traced to a group of 14th-century scholars at Oxford (who called it the ‘Mertonian mean speed theorem’), and the French bishop and scholastic philosopher Nicholas Oresme, who came up with a similar method.
Ossendrijver told CWA, ‘It is possible that the method was also used for other planets. However, Jupiter was of special significance in the city of Babylon: it was the astral manifestation of Marduk (Bel), the Babylonian supreme god, and the astronomers in Babylon who wrote these tablets were probably employed by that temple.’