Al-Khwarizmi and the book that named algebra
A practical handbook on inheritance and trade gave mathematics a new word, and a new way to solve for the unknown.
Around 820, Muhammad ibn Musa al-Khwarizmi wrote a short book on calculation by completion and balancing. Its Arabic title gave us the word algebra, from al-jabr.1
The full title is often given as al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala.
Completing the square
His best-known example asks for a square and ten of its roots that together make thirty-nine. He draws the square, adds strips along its sides, completes the larger square and reads off the answer: the root is three.
- Start with a square whose side is the unknown, x. Its area is x².
- Ten roots, 10x, are split into two strips of five, laid along two sides of the square.
- One small square is missing from the corner: five by five, so twenty-five.
- Add it to both sides: 39 and 25 make 64, a square whose side is 8. Take away the 5, and x is 3.
A name that traveled
His name, written Algoritmi in Latin, became the word algorithm. Few authors have lent both their title and their name to the language.2
The Latin form comes from translations of his book on Hindu–Arabic numerals.