Ancient Babylonian astronomers calculated Jupiter’s position from the area under a time-velocity graph

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Science  29 Jan 2016:
Vol. 351, Issue 6272, pp. 482-484
DOI: 10.1126/science.aad8085

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Babylonian astronomers tracked Jupiter

Ancient Babylonian astronomers developed many important concepts that are still in use, including the division of the sky into 360 degrees. They could also predict the positions of the planets using arithmetic. Ossendrijver translated several Babylonian cuneiform tablets from 350 to 50 BCE and found that they contain a sophisticated calculation of the position of Jupiter. The method relies on determining the area of a trapezium under a graph. This technique was previously thought to have been invented at least 1400 years later in 14th-century Oxford. This surprising discovery changes our ideas about how Babylonian astronomers worked and may have influenced Western science.

Science, this issue p. 482


The idea of computing a body’s displacement as an area in time-velocity space is usually traced back to 14th-century Europe. I show that in four ancient Babylonian cuneiform tablets, Jupiter’s displacement along the ecliptic is computed as the area of a trapezoidal figure obtained by drawing its daily displacement against time. This interpretation is prompted by a newly discovered tablet on which the same computation is presented in an equivalent arithmetical formulation. The tablets date from 350 to 50 BCE. The trapezoid procedures offer the first evidence for the use of geometrical methods in Babylonian mathematical astronomy, which was thus far viewed as operating exclusively with arithmetical concepts.

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