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Cubic Equations Table | MS 3048

CUBIC EQUATIONS TABLE

MS 3048
MS Short Title CUBIC EQUATIONS TABLE
Text TABLE WITH DATA FOR SOLVING CUBIC EQUATIONS, IN THE SUMERIAN SEXAGESIMAL SYSTEM
Description MS on clay, probably Larsa, Babylonia, 19th c. BC, 1 tablet, 7,6x4,4x2,3 cm, 3 columns, 30 lines in cuneiform script.
Context The only similar text known before is a Late Babylonian table text, where the numbers m at left take the values nxnx(n+1). Problems of the mentioned type are known from a large Old Babylonian clay tablet (BM 85200+VAT 6599).
Commentary Every line of the table says, "m has the root n". The numbers n at right take the values 1 to 30. The numbers m at left take the corresponding values nx(n+1)x(n+2). In the 6th line, for instance, n = 6 and m = 6x7x8 = 336 = 5x60 + 36. The table was probably used to set up a series of problems leading to cubic equations guaranteed to have integers as solutions. The problems would have been of the form "An excavated room. Its length equals its width plus 1 cubit. Its height equals its length. Its volume plus its bottom area is ... (a given number)."
Published Jöran Friberg: A remarkable Collection of Babylonian Mathematical Texts. Springer 2007. Sources and Studies in the History of Mathematics and Physical Sciences. Manuscripts in the Schøyen Collection, vol. 6, Cuneiform Texts I. pp. 56, 62-63.
Place of origin Babylonia
Dates ca 19c BC