# 820 Algebra

## Algebra

Considering only positive numbers, al-Khwārizmī divided linear and quadratic equations into six basic types and showed how to solve them. Although his book was likely a compendium of existing knowledge, it stands as the first work to feature a strictly algebraic mathematical approach so that Latin translations of it in the 12th century introduced to the West not only the math but the terms algebra and, based on al-Khwārizmī’s name, algorithm.

## Operations

The al-ğabr operation is moving a negative quantity on one side of the equation to a positive quantity on the other side. This restores negative quantities which Islamic mathematicians at the time did not find useful. The al-Muqabala operation is subtracting the same positive quantity from both sides. This balancing or corresponding act reduces the equation to the fewest terms.

## Variable unknown

Let x be an unknown quantity of a variable thing, unlike the E in E = mc2. When I say x, I mean anything that’s consistent, not necessarily energy. Let x = f(y), where f is an arbitrary function that depends on a variable y. Our function could return an interest, the return on a bond, or the percentage of profit. In fact, it could be any useful operation, anything that’s smart and practical. Now, indeed, we are moving to a higher order of math and intellect.

Unfamiliarity with the notation can make a person feel as though a mathematical topic is beyond their intellectual powers when it is not.