The Liber Abaci
-Chrissie

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            It would be a difficult task to pass through one’s day without seeing any of the numerals 0-9. By using just these ten symbols and their position in relation to each other, we can indicate any amount and do any type of mathematical work one can imagine. Modern numerals are based on those of the Hindu-Arabic system, which was derived from the much older Brahmi numeral system, dating to around the third century BCE, which was, in turn, based on yet another older system. These used the numerals 1 through 9 and had a blank space where a zero would be used in the modern day. This structure was then adapted for use by Arab mathematicians in the ninth century; they added the zero as a placeholder to reduce confusion. From this, it came to the attention of mathematicians in Western Europe via Al-Andalus, Muslim-controlled Spain, in the tenth century. These numerals do not, however, become widely used in Western Europe until after the publication of the Liber Abaci by Leonardo of Pisa (better known as Fibonacci) in 1202. It was not that they were unknown in Europe, but it was primarily mathematicians who used them. The average person used Roman numerals for their day-to-day number needs.

            Leonardo of Pisa was the son of an Italian merchant who did a great deal of work in the city of Bugia, in what is now Algeria. Along this coast of the Mediterranean, the Hindu-Arabic system was used wherever numbers were needed, whether in abstract or theoretical mathematics or for more mundane activities like calculating prices. Having worked in both methods, Leonardo saw the potential value of the Hindu-Arabic system for Europeans who weren’t mathematicians. He wrote the Liber Abaci (The Book of the Abacus or The Book of Calculation) to serve as a guide for using Hindu-Arabic numerals in such common areas as bookkeeping, calculation of interest, weights and measures, and many other purposes. Leonardo’s work was well-received, its usefulness immediately obvious to anyone who worked with numbers in a practical setting.

            The book is split into four sections: the first introduced the system and explains its value in relation to other methods of working with numbers. The second addresses commercial use, giving examples of how the method can be used for calculating currency exchanges and interest, to manage inventory, and to keep a running log of debits and credits on an account. The rest of the book deals with geometry, algebra, irrational numbers, and many other elements of higher mathematics, including the Fibonacci sequence for which the man is best-known today.

            No copies of the original 1202 edition still exist, the oldest is a revised edition from 1227. Oddly, despite its importance, it remained in manuscript (handwritten) format until the mid-nineteenth century, when an edition in the original Latin was printed by Baldassarre Boncompagni in 1857. This is, perhaps, because its ideas were so quickly and easily integrated into other texts, causing the original, important though it is, to become obsolete.