SOLUTION: Why is it called algebra? Why is algebra useful? What does an algebra problem look like? How are algebra problems different?

Question 139568: Why is it called algebra?
Why is algebra useful?
What does an algebra problem look like?
How are algebra problems different?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Origin of the word Algebra
Some writers on the history of mathematics call al-Khwarizmi as the father of algebra, other give that title to Diophantus. Al-Khwarizmi's algebra is undoubtedly foundation and cornerstone of the sciences. He was the first to teach algebra in an elementary form and for its own sake.
In his own words, al-Khwarizmi described what he wanted to teach with his work Hisab al-jabr w'al-musqabala :
"... what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, lawsuits, and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computations, and other objects of various sorts and kinds are concerned."
Al-Khwarizmi's algebra was more involved with what we today call algebraic manipulation, Diophantus' algebra was more involved with the theory of numbers.
One of the most important of mathematical writings on Algebra were precisely the works of the Persian born al-Khowarizmi, who around 825 AD wrote in Baghdad a book mentioned above, the famous Hisab al-jabr w-al-musqabalah, which means "Science of the Reunion and the Opposition" or in more modern terms "science of the transposition and cancellation". The book became influential in the reintroduction of the subject matter into Europe through the translations into Latin and later colloquial languages.
The terms al-jabr and al-musqabalah refer to the following processes:
Al-jabr (= the transposition) of terms; means that, for example that an equation which starts as

would be transformed into

and further this would be by the process called al-musqabalah (= the cancellation) further transformed into

The term algebra was eventually accepted as one and unifying term to represent all that was meant under al-jabr w-al-musqabalah.
So you see: what we adopted as the word for algebra is really only one half of what al-Khwarizmi wanted to call it. We call this algebra, but may as well call it almuqabala.

That should get you started. You still have some work to do to answer all of the questions.

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