A Geometric Algorithm with Solutions to Quadratic Equations in a Sumerian Juridical Document from Ur III Umma

"In the late 1920’s the existence of both Old and Late Babylonian mathematical cuneiform texts with solutions to second-degree problems were discovered at O. Neugebauer’s path-breaking history of mathematics seminar in Göttingen. The announcement of the discovery was received with “immense amazement” (Høyrup 2002: 1, fn. 2). In this paper will be discussed, for the first time, the existence of an even older cuneiform text, YBC 3879, a juridical field division document from the Sumerian Ur III period, in which unequivocally appear solutions to a series of second-degree problems. Ironically, a copy of the text in question was published (although without any translation or commentary) in a volume of Miscellaneous Inscriptions in the Yale Babylonian Collection by A. T. Clay in 1915, that is more than a decade before the mentioned sensational discovery at Neugebauer’s seminar!"