Liber Abaci: Translated by Laurence Sigler

Liber Abaci

Written in Latin, Leonardo of Pisano’s Liber Abaci (Book of Calculation) (1228) was inaccessible to most people for nearly 800 years, until 2002, when American mathematics professor Lawrence Sigler translated Baldassarre Boncompagni’s Latin edition, Scritti di Leonardo Pisano, Vol. 1 (Rome, 1857). Sigler’s Translation into Modern English of Leonardo Pisano’s Book of Calculation provides the first (and only) complete English translation of Fibonacci’s Liber Abaci with parallel commentary in modern mathematical notation.

Leonardo began Liber Abaci with a brief dedication to Michael Scott, who was a philosopher and scholar in the court of Emperor Frederick II; he then inexplicably provided autobiographical information describing how and why he wrote the book – so that the Latin people would no longer lack knowledge of the magnificent art and science of Hindu calculation methods.

Without further ado, the mathematician gets down to business by introducing the nine digits (and zero) used by the Hindus to represent numbers. Early chapters contain exhaustive treatments of problems using multiplication, addition, subtraction and division of whole numbers, integral numbers, and fractions; later chapters present difficult algebraic and geometric problems and solutions, all without algebraic symbolism. In Chapter Twelve there is the famous problem having to do with the reproduction rate of rabbits from which the Fibonacci sequence emerges. The last few chapters address topics and strategies of particular interest to businessmen, such as principal valuation methods, bartering, company structure, and the alloying of money.

Lawrence’s style mirrors Leonardo’s, which was straight-forward and easily comprehensible. Moreover, he carefully provided word-for-word translation of the math text with sufficient details and definitions, wholly devoid of extraneous intrusion in the form of personal editorial or commentary. Lawrence’s final chapter, Chapter 16, contains many helpful explanatory notes.

About the Laurence Sigler

Lawrence (who also provided an English translation of Leonardo’s much shorter algebra book, Liber Quadratorum (Book of Squares) (1987) provides no information about himself and, after extensive research, the only thing (besides titles of his writings) I could learn about him was that he was a mathematics professor at Bucknell University in Pennsylvania. Keith Devlin, who met Professor Sigler’s widow, provides a bit more information about him in his book, Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World (2017). My conjecture is that Lawrence shares the same humility as Leonardo, and he would consider the most important thing to know about him is that he made Leonardo’s encyclopedic work accessible to people who were without knowledge of the genius of one of the world’s most important mathematicians.

Sigler, Laurence. Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation (Sources and Studies in the History of Mathematics and Physical Sciences).

Springer, 2003
Paperback: 638 pages; illustrations   
ISBN-10: 9780387407371
ISBN-13: 978-0387407371