NEW YORK, N.Y.- Key parts of the Liber Abaci, the work that shaped the course of history by introducing Arabic numerals to the west, are to be sold at Bonhams New York on 22 June. They feature in a rare 15th century manuscript estimated at between $120,000-180,000 (£75,000 – 110,000).

The Liber Abaci or Book of Calculation is by Leonardo Pisano Bigollo or Fibonacci, considered by many as one of the most talented western mathematicians of the Middle Ages. Fibonacci is widely credited with bringing the Hindu-Arabic numeral system to the western world.

Within the text of the Liber Abaci, Fibonacci explains the benefits of Arabic numerals and the symbol for zero by applying them to the practical world of book-keeping, weights and measures, and trade. His theory popularized Arabic numerals by appealing to tradesmen and academics and eventually convincing the public of the superiority of the new numerals. It was Fibonacci’s text that eventually paved the way for modern mathematical equations, sequences used in computer programming and financial markets.

The Fibonacci Sequence, where each successive number is the sum of the two preceding numbers (1+1=2, 2+1=3, 3+2=5), is used in global financial markets and relates to the Golden Ratio, which appears in modern aircraft, art, architecture and music as well as playing a key role in the plot of Dan Brown’s The Da Vinci Code.

The manuscript for sale contains the complete text of the section of Liber Abaci known as Flos or “The Flower,” which is the most advanced sections of Liber Abaci, dealing with calculus, and geometrical and algebraic methods for solving quadratic equations.

This manuscript was produced in Italy and written in Latin. The Liber Abaci first appeared in 1202, in manuscript form, and only 12 copies of the manuscript from the 13th to the 15th century have been traced in European libraries – many of them in the Vatican.

Around 1225, Fibonacci attended the court of the Holy Roman Emperor Frederick II at the request of His Holiness. The Emperor wanted to meet with Europe’s leading mathematician. It was during this encounter that Frederick’s court mathematician challenged Fibonacci to solve three problems, one of which was borrowed from a text by Omar Khayyam of Rubaiyat fame – the text was called Al-jabr (“Algebra”). It is in the Flos chapters of the Liber Abaci that Fibonacci solves the problems.

Bound with the Liber Abaci is a second manuscript from a century earlier, which includes a text by Boethius.

Preview: June 18-21, 2011, New York
Auction: June 22, 2011, New York