IM 67118

IM 67118, also known as Db2-146, is an Old Babylonian clay tablet in the collection of the National Museum of Iraq that contains the solution to a problem in plane geometry concerning a rectangle with given area and diagonal. In the last part of the text the solution is proved correct by means of the Pythagorean theorem. The steps of the solution are believed to represent cut-and-paste geometry operations involving a diagram from which, it has been suggested, ancient Mesopotamians might, at an earlier time, have derived the Pythagorean theorem.


The tablet was excavated in 1962 at Tell edh-Dhiba'i, an Old Babylonian settlement near modern Baghdad that was once part of the kingdom of Eshnunna, and was published by Taha Baqir in the same year.[1][2] It dates to approximately 1770 BCE (according to the middle chronology), during the reign of Ibal-pi-el II, who ruled Eshnunna at the same time that Hammurabi ruled Babylon.[3] The tablet measures 11.5×6.8×3.3 cm.[4] Its language is Akkadian, written in cuneiform script. There are 19 lines of text on the tablet's obverse and six on its reverse. The reverse also contains a diagram consisting of the rectangle of the problem and one of its diagonals. Along that diagonal is written its length in sexagesimal notation; the area of the rectangle is written in the triangular region below the diagonal.[5]

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