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**Fibonacci’s Liber abaci. A translation into modern English of Leonardo Pisano’s Book of calculation. Transl. from the Latin and with an introduction, notes and bibliography by L. E. Sigler.**
*(English)*
Zbl 1032.01046

Sources and Studies in the History of Mathematics and Physical Sciences. New York, NY: Springer (ISBN 0-387-95419-8/hbk). viii, 636 p. (2002).

Leonardo Pisano, known today to mathematicians all over the world by the name of Fibonacci was a citizen of the city-state of Pisa. Liber abaci, or the Book of Calculation, appeared first in 1202, offers an encyclopedic treatment of much of the known mathematics of the thirteenth century on arithmetic, algebra and problem solving.

The book is divided into 15 chapters with a preface. In the preface Leonardo states how in his travels and studies he has found the Hindu number system and its methods of calculation to be superior to all other methods and that he wishes to bring these to the Italian people in his work. The book begins with ten numerals of the Hindu number system (including zero) and explains our familiar decimal place system. In the following chapters algorithms for multiplication, addition and subtraction of whole numbers, divisions of small numbers and simple fractions, and so forth are considered. These form a theoretical basis for solving the following problems: Travellers with expenses and profits, horse buying, the sale of money already bartered, the purchase of money according to rule, mixture of fruits, gold, grain, birds and so forth. In the last chapter the Pythagorean theorem is used and also simple areas and volumes are found.

Most of the procedures for solving the examples are tabulated on the margines (more than 800 illustrations altogether). At the head of each chapter a table of contents for his entire book with more detailed list of contents is given. The validity of the methods he has used is based upon Book II and Book X of Euclid’s Elements.

This book represents the first modern edition of this work and with respect to completeness the only translation that is available in a modern language. Up to now only B. Boncompagni’s 1857 Latin edition did exist.

Therefore the book will be of interest not only to historians of science, but to all mathematicians and mathematics teachers interested in the origins of their methods.

The book is divided into 15 chapters with a preface. In the preface Leonardo states how in his travels and studies he has found the Hindu number system and its methods of calculation to be superior to all other methods and that he wishes to bring these to the Italian people in his work. The book begins with ten numerals of the Hindu number system (including zero) and explains our familiar decimal place system. In the following chapters algorithms for multiplication, addition and subtraction of whole numbers, divisions of small numbers and simple fractions, and so forth are considered. These form a theoretical basis for solving the following problems: Travellers with expenses and profits, horse buying, the sale of money already bartered, the purchase of money according to rule, mixture of fruits, gold, grain, birds and so forth. In the last chapter the Pythagorean theorem is used and also simple areas and volumes are found.

Most of the procedures for solving the examples are tabulated on the margines (more than 800 illustrations altogether). At the head of each chapter a table of contents for his entire book with more detailed list of contents is given. The validity of the methods he has used is based upon Book II and Book X of Euclid’s Elements.

This book represents the first modern edition of this work and with respect to completeness the only translation that is available in a modern language. Up to now only B. Boncompagni’s 1857 Latin edition did exist.

Therefore the book will be of interest not only to historians of science, but to all mathematicians and mathematics teachers interested in the origins of their methods.

Reviewer: J.Fiamčik (Prešov)