Different Concepts of Equations in The Nine Chapters on Mathematical Procedures and in the Commentary on it by Liu Hui (3rd century)

Karine Chemla (1)

1 SPHERE (UMR_7219) - Sciences, Philosophie, Histoire

The Han text, The Nine chapters on Mathematical Procedures, contains two operations which can be identified as equations: chapter VIII is devoted to the solution of systems of simultaneous linear equations, and problem 20 in chapter IX is solved by means of a quadratic equation. Are these operations, which we regard as being of the same kind conceived of as connected with one another in the Han classic and in its commentary by Liu Hui? This is the question I would like to raise in the present paper. I shall show that, even though these two kinds of equation have features in common, they present essential differences. Moreover, a brief comparison with equations as dealt with in al-Khwarizmi's Concise Book on the Computation of algebra and al-muqabala will show affinities between these and equations as treated in the eighth of The Nine Chapters rather than with the quadratic equation of chapter IX. In order to prove my point, I shall first examine the content of chapter VIII from this point of view, after which I shall compare the concept of the equation elaborated there with that of the quadratic equation which emerges from chapter IX. Finally, I shall compare both kinds to equations as conceived by al-Khwarizmi.

Mots clés: Concise Book on the Computation of algebra and al-muqabala; al-Khwarizmi; linear equations; quadratic equations; The Nine chapters on Mathematical Procedures; Liu Hui

Domaines: Histoire; Histoire et perspectives sur les mathématiques [math.HO]

Karine Chemla. Different Concepts of Equations in The Nine Chapters on Mathematical Procedures and in the Commentary on it by Liu Hui (3rd century). Historia Scientarum, 1994, 4 (2), pp.113-137. ⟨halshs-00873649⟩