# Bisecting the trapezoid: tracing the origins of a Babylonian computation of Jupiter’s motion

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## Abstract

Between ca. 400 and 50 BCE, Babylonian astronomers used mathematical methods for predicting ecliptical positions, times and other phenomena of the moon and the planets. Until recently these methods were thought to be of a purely arithmetic nature. A new interpretation of four Babylonian astronomical procedure texts with geometric computations has challenged this view. On these tablets, Jupiter’s total distance travelled along the ecliptic during a certain interval of time is computed from the area of a trapezoidal figure representing the planet’s changing daily displacement along the ecliptic. Moreover, the time when Jupiter reaches half the total distance is computed by bisecting the trapezoid into two smaller ones of equal area. In the present paper these procedures are traced back to precursors from Old Babylonian mathematics (1900–1700 BCE). Some implications of the use of geometric methods by Babylonian astronomers are also explored.

## Notes

### Acknowledgements

The Trustees of the British Museum are acknowledged for permission to study and publish the tablets kept in the British Museum. Christopher B.F. Walker is acknowledged for making available his catalogue of astronomical fragments in the Babylon collection of the British Museum.

## Compliance with ethical standards

## Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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