Open Access Book: Algebra in Cuneiform: Introduction to an Old Babylonian Geometrical Technique

Algebra in Cuneiform: Introduction to an Old Babylonian Geometrical Technique
By Jens Høyrup

 

This textbook analyzes a number of texts in “conformal translation,” that is, a translation in which the same Babylonian term is always translated in the same way and, more importantly, in which different terms are always translated differently. Appendixes are provided for readers who are familiar with basic Assyriology but otherwise philological details are avoided. All of these texts are from the second half of the Old Babylonian period, that is, 1800–1600 BCE. It is indeed during this period that the “algebraic” discipline, and Babylonian mathematics in general, culminates. Even though a few texts from the late period show some similarities with what comes from the Old Babylonian period, they are but remnants. Beyond analyzing texts, the book gives a general characterization of the kind of mathematics involved, and locates it within the context of the Old Babylonian scribe school and its particular culture. Finally, it describes the origin of the discipline and its impact in later mathematics, not least Euclid’s geometry and genuine algebra as created in medieval Islam and taken over in European medieval and Renaissance mathematics.

Preface

1Introduction: The Issue – and Some Necessary Tools

2Techniques for the First Degree

3The Fundamental Techniques for the Second Degree

4Complex Second-degree Problems

5Application of Quasi-algebraic Techniques to Geometry

6General Characteristics

7The Background

8Origin and Heritage

9A Moral

Appendix A: Problems for the Reader

Appendix B: Transliterated Texts

Bibliographical Note