Wednesday, February 4, 2009
Algebra---->Muhammad ibn Musa Al-Khwarizmi
Al-Khwarizmi introduces the main topic of this first section of his book, namely the solution of equations. His equations are linear or quadratic and are composed of units, roots and squares. For example, to al-Khwarizmi a unit was a number, a root was x, and a square was x2. However, although we shall use the now familiar algebraic notation in this article to help the reader understand the notions, Al-Khwarizmi's mathematics is done entirely in words with no symbols being used.
He first reduces an equation (linear or quadratic) to one of six standard forms:
1. Squares equal to roots.
He first reduces an equation (linear or quadratic) to one of six standard forms:
1. Squares equal to roots.
2. Squares equal to numbers
.3. Roots equal to numbers.
4. Squares and roots equal to numbers; e.g. x2 + 10 x = 39.
5. Squares and numbers equal to roots; e.g. x2 + 21 = 10 x.6. Roots and numbers equal to squares; e.g. 3 x + 4 = x2.
The reduction is carried out using the two operations of al-jabr and al-muqabala. Here "al-jabr" means "completion" and is the process of removing negative terms from an equation. For example, using one of al-Khwarizmi's own examples, "al-jabr" transforms x2 = 40 x - 4 x2 into 5 x2 = 40 x. The term "al-muqabala" means "balancing" and is the process of reducing positive terms of the same power when they occur on both sides of an equation. For example, two applications of "al-muqabala" reduces 50 + 3 x + x2 = 29 + 10 x to 21 + x2 = 7 x (one application to deal with the numbers and a second to deal with the roots).
Jiayoufann thought hard on 4:16 PM.
