###### Clay tablets like this one, describing Halley's Comet in 164 BCE, record the Babylonians' advanced astronomical observations. | Flickr/ Gavin Collins

Analysis of ancient Babylonian tablets reveals that the tablets' makers used geometry to calculate the position of Jupiter — using a technique that was previously believed to have been developed at least 1400 years later in 14^{th} century Europe. The findings are published in the 29 January issue of *Science*.

Babylon was an ancient and powerful epicenter in the Middle East. It was rich in many ways, including in scholars and particularly astronomers and mathematicians. Historians rely mostly on clay tablets that record the scholarly work of this era. While several hundred fragmented tablets exist, the analysis of just five of them reveals advanced geometry techniques used to calculate the position of Jupiter through time and space.

"All five tablets discussed in *Science* contain instructions on how to compute the celestial position of Jupiter for a specific period of 60 days after Jupiter becomes visible in the night sky," said Mathieu Ossendrijver of the Humboldt University of Berlin. "On four of them, these instructions mention a geometrical figure, a trapezoid. As it turns out, this trapezoid depicts how Jupiter's velocity changes with time over the 60 days."

Before these results were published, researchers knew that four of the tablets referred to a trapezoid shape, but the context for mentioning the shape was unclear. The deciphering of the fifth tablet was key to understanding the references to the trapezoid in the other tablets, revealing just how advanced ancient Babylonian astronomers were.

The texts contain geometrical calculations based on a trapezoid's area, and its long and short sides. The ancient astronomers also computed the time when Jupiter covers half of this 60-day distance by partitioning the trapezoid into two smaller ones of equal area.

The tablets were most likely written in Babylon between 350 and 50 BCE, making them the earliest known examples of using geometry to calculate positions in time and space. "Ancient Greek astronomers used a lot of geometrical techniques, but the geometrical figures that they use are always situated in a real space, with either two- or three-spatial dimensions," Ossendrijver explains. "The Babylonian geometrical methods discussed here involve figures that are defined in a more abstract mathematical space obtained by drawing velocity against time, almost in a modern fashion."

Since the ancient Greeks were using geometry but not to calculate time and velocity, researchers believed that Europeans in the 1300s were the first to develop such a combination of calculations. However, these tablets redefine the history books, revealing that European scholars in Oxford and Paris in the 14th century were, in fact, centuries behind their ancient Babylonian counterparts.