The Compendious Book on Calculation by Completion and Balancing

Muhammad ibn Musa al-Khwarizmi wrote this book in Baghdad around 820. Al-jabr in its title means completing an equation by moving negative terms across, and al-muqabala means cancelling like terms on both sides.

What was new

Al-Khwarizmi did not just solve individual problems. He sorted equations into types and gave a method for each, with geometric proofs. He also devoted sections to practical uses in inheritance, measurement and trade.

The road to Europe

The book was translated into Latin in the twelfth century, and through it the word algebra entered European languages.