Algebraic Equations East and West until the Middle Ages
Résumé
I sketch here a history of quadratic equation aiming at illustrating the potential fruitfulness of a non-linear history of algebraic equations. I show how a combination of three approaches is required to conduct such an inquiry in that particular case. Comparative history: in Babylonian, Chinese, and Greek sources, what we might recognize as quadratic equations manifests itself in very different ways depending on the corpus of texts considered. Conceptual history: this remark highlights that, in Antiquity, there were different concepts of equation available. We find respectively equation seen as problems (Mesopotamian sources), as operation depending on root extraction (Chinese sources), and as assertion of an equality (al-Khwarizmi). Historical documents show that, instead of one eliminating the other concepts, the history of algebraic equations evidences moments of synthesis between them. In particular, the work On equations by Sharaf al-Din al-Tusi at the end of the 12th century, seems to represent such a synthesis. We must attempt to understand the work required by such a synthesis and what its results were. Such a work probably depended on complex connections between Arabic, Chinese, and Indian knowledge cultures. This is where the third approach is required: tackling the historical problem of transmission.
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