Fibonacci

If anyone knows how to extract the square root of a non-square number, he will be able to find the side of a square whose area is not a perfect square.

I have been led to this by the desire to demonstrate to the people of Pisa, and to the whole world, the utility of the Indian method of calculation.

The nine Indian figures are: 9 8 7 6 5 4 3 2 1. With these nine figures, and with the sign 0 which is called zephirum in Arabic, any number can be written.

A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair from the second month on?

And so, from the first month, one pair remains; in the second month, two pairs; in the third, three pairs; in the fourth, five pairs; in the fifth, eight pairs; in the sixth, thirteen pairs; in the seventh, twenty-one pairs; in the eighth, thirty-four pairs; in the ninth, fifty-five pairs; in the tenth, eighty-nine pairs; in the eleventh, one hundred forty-four pairs; in the twelfth, two hundred thirty-three pairs.

For the more one knows, the more one can do.

I have striven to insert in this work all the rules of arithmetic and geometry, which I have found to be useful and necessary for merchants and others.

And so, in order that the Latin people should not be deprived of this knowledge, I have composed this work.

The method of the Indians surpasses any known method of calculation. It is a wonderful method. They do their computations using nine figures and the zero.

For this reason, I have taken pains to present the entire subject of arithmetic in a clear and complete manner.

After my father's appointment by his country as notary public in the customs house of Bugia, as a boy I was introduced to him and there I learned the art of the Indians' nine symbols through amazing teaching.

The more I learned, the more I understood the utility of this method above all others.

And I have taken care to present the whole subject in a clear and complete manner, so that those who wish to learn it may do so without difficulty.

I have also added some geometrical demonstrations, which are necessary for the understanding of some of the rules.

Indeed, all the problems that I have solved in this book are taken from the practice of merchants.

And I have striven to make this work useful to all who wish to learn the art of calculation.

Therefore, I have composed this book, which I have called Liber Abaci, in order that the Latin people should not be deprived of this knowledge.

And if anyone should find any error in this work, I beg him to correct it, for I am but a man, and liable to err.

I have also included some problems that are not directly related to commerce, but which are useful for exercising the mind.

The value of a number is not changed by adding or subtracting zero.