Unknown Quantity

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…Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala ("A Handbook of Calculation by Completion and Reduction"). John Derbyshire examines al-Khwarizmi's work in chapter 3 of Unknown Quantity: A Real and Imaginary History of Algebra [ISBN 978-0-452-28853-9], which I just finished reading a few days ago. The first part of al-Khwarizmi's book concerns finding the roots of first- and second-order polynomials of one unknown. He classified the polynomials into 6 fundamental types, with all positive coefficients. Keep in mind, that negative numbers did not exist at the time, though subtraction did. He showed how to manipulate polynomials into a suitable one of the 6 types by adding a term (al-jabr, completing) or subtracting a term (al-muqabala, reducing). Says Derbyshire, "al-Khwarizmi has no literal symbolism--no way to lay out equations in letter…