*Fibonacci’s Liber Abaci: Leonardo Pisano’s Book of Calculation*, Laurence Sigler, 2003, 636 pp. $49.95, paper. ISBN 0-387-40737-5. Springer-Verlag, New York, Inc., 175 Fifth Ave., New York, NY 10010. (800)-SPRINGER. [email protected].

Leonardo of Pisa, commonly known as Fibonacci, wrote his *Liber abaci* [*Book of Calculation*] in 1202 and published a revised and expanded edition in 1228. This encyclopedic work was intended to convey newfound mathematical knowledge and computational techniques to an Italian reading audience. The weighty tome introduced the “Hindu-Arabic” numerical system and its computing algorithms to its readers as well as algebraic solution techniques for a variety of problems. Leonardo acquired this knowledge from Arab sources. Drawing freely on the works of al-Khowarizmi, Abu Kamil and al-Karaji, he surveyed a wide scope of applied problems. These problems considered such topics as: cost and profit; barter; partnership; investment; alligation; mensuration and simple geometry. In content and format Liber abaci established a genre for European commercial arithmetic books for the next four centuries. Included in its problem collection is the rabbit breeding situation that gave rise to what is now known as the “Fibonacci sequence”. The *Liber abaci* is a milestone in the evolution of western mathematics, one that remained untranslated into a modern language until now.

During the period 1857-1862, the Italian bibliophile and medieval mathematical historian, Boldassarre Boncompagni compiled a two-volume edition of Leonardo’s work written in modern Latin. This is the source for L. E. Sigler’s English translation. Laurence Sigler was a Professor of Mathematics at Bucknell University and an amateur Latinist whose previous translation of Leonardo’s *Liber quadratorum* [*Book of Squares*] (1987) was welcomed by mathematical historians. Although Boncompagni’s work has been approached with caution by other researchers, Sigler was confident with its factual information and his undertaking provides a valuable resource for a better understanding of medieval European mathematics. The algebra considered is rhetorical in form and “wordy” in translation. Indeed, the text is word and concept dense, which makes for difficult reading. Explanations must be worked through with the assistance of a pencil and paper. The translation is prefaced by a brief introduction. A more detailed commentary on this work would be welcomed. This translation of *Liber abaci* will serve as a serious research tool for students of medieval European mathematics and provide a valuable reference for any undergraduate mathematics library.

Frank J. Swetz, Professor Emeritus, The Pennsylvania State University