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

Abstract

In the late 1920’s the existence of both Old and Late Baby-lonian mathemat ical cuneiform texts with solutions to second-degree problems were discovered at O. Neu gebauer’s path-breaking history of mathematics seminar in Göttin-gen. The announcement of the discovery was received with “immense amazement ” (Høyrup 2002: 1, fn. 2). In this paper will be discussed, for the fi rst time, the existence of an even older cunei form text, YBC 3879, a juridical fi eld 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 ques-tion was published (although without any translation or commen tary) in a volume of Miscellaneous Inscriptions in the Yale Babylonian Collection by A. T. Clay in 1915, that