Origins of Two Familiar Math Terms

In the 800's the mathematician Abu Ja'far Muhammad ibn Musa al-Khwarizmi wrote, among other works, two books on the subjects of arithmetic and algebra. In the book, Concerning the Hindu Art of Reckoning, al-Khwarizmi used the Hindu numeral system. However, European readers inaccurately consider the number system as Arabic numerals. The use of Hindu numerals became known as algorithm, derived from the name al-Khwarizmi. Today, the word algorithm is used for any process or procedure.

Al-Khwarizmi's other book, The Compendious Book on Calculation by Completion and Balancing, contained a method known as al-jabr. This is the method of removing negative amounts from an equation by adding that amount to each side. That is, for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 = x- 2x^2} one would apply al-jabr by adding Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2x^2} to both sides to get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3x^2 = x} . The term algebra is derived from the word al-jabr.

[References]:
Pickover, C. A. (2008), The Math Book. New York, NY: Sterling Publishing Co., Inc.
Boyer, C. B. (1991), A History of Mathematics. New York, NY: John Wiley & Sons, Inc.