The Compendious Book on Calculation by Completion and Balancing
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Equations become objects handled by a general procedure rather than problems solved one by one, and the book's title for that procedure gives algebra its name.
- every quadratic reduced to six standard forms with a rule for each
- a general teachable procedure in place of case-by-case ingenuity
- geometric demonstration supplied for each algebraic rule
- practical inheritance and commercial problems as the working material
Al-Khwarizmi reduces every equation of the first and second degree to one of six standard forms, then gives a rule for each, with geometric demonstrations that the rule is sound. The two operations of the title are moving a subtracted quantity to the other side and cancelling like terms on both. The problems worked are inheritance shares, land measurement and trade, because those are what people brought. Its importance is method: where Greek mathematics solved particular cases with brilliance, this is a procedure that can be taught to anyone competent.
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