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He didn't invent, but rather used the word, "al-jabr," which means "restoration" in Arabic, to describe his method of defining an unknown quantity as a variable and then manipulating it within an equation to arrive at its value. In other words, "al-jabr" means to perform an algebraic process, hence the word "algebra" being derived from it.
His name (Al-Khwarizmi) is the root for the word "algorithm" although Al-Khwarizmi himself did not coin the word.
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