The Little Book of Mathematical Principles, Theories & Things. Robert Solomon

(The Book of Shifting and Balancing)

      Al-Khwarizmi (c. 780–c. 850 AD)

      A comprehensive guide to solving quadratic equations.

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      Al-Khwarizmi’s book describes six types of quadratic equation and solves them in a methodical manner.

      Kitab wa al jabr wa al muqabalah means: “The Book of Shifting and Balancing.” With an equation you shift terms from one side to another, and then you balance the terms collected on one side.

      Say Al jabr quickly. This book is where the word algebra comes from. It is a long way from the algebra studied in schools today: for example, there is no use of letters such as x to stand for an unknown. Indeed, equations are written out in terms of words rather than symbols.

      Al-Khwarizmi considers six separate types of quadratic equation, though nowadays the single quadratic formula covers them all. In his time there were no negative numbers, and so x² – 5x = 6 had to be treated differently from x² + 5x = 6.

      The book contains no startling new discoveries. Its virtue consists in its systematic collection of different results and its methodical treatment of them, in an algebraic rather than a geometric way.

      See: Quadratic Equations, pages 11–12