Lengths, Widths, Surfaces A Portrait of Old Babylonian Algebra and Its Kin [Paperback]

In this examination of the Babylonian cuneiform algebra texts, based on a detailed investigation of the terminology and discursive organization of the texts, Jens H?yrup proposes that the traditional interpretation must be rejected. The texts turn out to speak not of pure numbers, but of the dimensions and areas of rectangles and other measurable geometrical magnitudes, often serving as representatives of other magnitudes (prices, workdays, etc...), much as pure numbers represent concrete magnitudes in modern applied algebra. Moreover, the geometrical procedures are seen to be reasoned to the same extent as the solutions of modern equation algebra, though not built on any explicit deductive structure.

In this examination of the Babylonian cuneiform algebra texts, based on a detailed investigation of the terminology and discursive organization of the texts, Jens H?yrup proposes that the traditional interpretation must be rejected. The texts turn out to speak not of pure numbers, but of the dimensions and areas of rectangles and other measurable geometrical magnitudes, often serving as representatives of other magnitudes (prices, workdays, etc...), much as pure numbers represent concrete magnitudes in modern applied algebra. Moreover, the geometrical procedures are seen to be reasoned to the same extent as the solutions of modern equation algebra, though not built on any explicit deductive structure.

I. Introduction / II. A New Reading / III. Select Textual Examples / IV. Methods / V. Further 'Algebraic' Texts / VI. Quasi-Algebraic Geometry / VII. Old Babylonian 'Algebra': A Global Characterization / VIII. The Historical Framework / IX. The 'Finer Structure' of the Old Babylonian Corpus / X. The Origin and Transformations of Old Babylonian Algebra / XI. Repercussions and Influences / XII. Index of Tablets / XIII. Index of Akkadian and Sumerian Terms and Key Phrases / XIV. Name Index / XV. Subject Index / XVI. Abbreviations and BlC