Muhammad ibn Musa al-Khwarizmi

When I considered what people generally want in calculating, I found that it always is a number.

I have discovered that the numbers are infinite, and that each number has a unique position.

The science of algebra is a science of balancing and completion.

This book contains the rules of algebra, which are the most elementary and useful rules for solving problems.

We will explain what is easy and what is difficult, so that the student may understand the principles of algebra.

The operations of algebra are three: addition, subtraction, and multiplication.

The unknown quantity is called the 'root' or 'thing'.

The square of the unknown quantity is called 'mal' or 'power'.

The number is called 'dirham' or 'constant'.

The purpose of this book is to teach the art of calculation by means of algebra.

I have composed this book on the calculation of al-jabr and al-muqabala, which is a concise treatise on the rules of calculation.

The science of algebra is a noble and useful science.

The rules of algebra are necessary for all who wish to understand the principles of calculation.

I have explained the rules of algebra in a clear and simple manner.

The solutions to problems are found by balancing and completing the equations.

The method of al-jabr is to remove negative terms from one side of the equation by adding them to the other side.

The method of al-muqabala is to reduce positive terms on both sides of the equation by subtracting equal amounts.

These two operations, al-jabr and al-muqabala, are the foundation of algebra.

I have provided examples for each type of equation to illustrate the methods.

The solutions to these problems are always rational numbers.