Fibonacci

Fibonacci appears in the Encyclopaedia of Islam under the names Leonardo and Leonard of Pisa. The articles read treat him as the European mathematician through whom a good deal of Arabic arithmetic, algebra and geometry reached Latin readers, and they cite his writings by title: the Liber abaci of 1202, the Liber quadratorum and the Practica geometriae. ^{1 4 5} The articles give no birth or death date for him and no account of his life, such as where he learned Arabic mathematics. This record therefore describes only how the Encyclopaedia connects his books to Arabic sources.

The article on al-jabr wa'l-muqabala traces how the name of al-Khwarizmi's science passed into Latin. It notes that Robert of Chester translated part of the algebra in 1145 and Gerard of Cremona made a second translation, and that in 1202 Leonard of Pisa used, in the Liber abaci, the expression "compositum et elmulchabale", a form of the Arabic pair of terms. ¹ The article on the invention of algebra gives the wider setting.

The article on Abu Kamil says he exercised considerable influence on the development of algebra in Europe through Leonard of Pisa and his followers. ⁶ It gives several concrete links:

• Both Abu Kamil and the Liber abaci treat indeterminate problems, in both cases using examples about birds. ²
• Abu Kamil shows how to add and subtract square roots that are irrational. The article notes that Leonard demonstrates the same method with the numbers 18 and 32, where Abu Kamil uses 18 and 8. ²
• The article records that Sacerdote showed Leonard knew Abu Kamil's treatise on the pentagon and decagon and used it extensively in the Practica geometriae. ²

In the article on al-Karaji, the author notes that systems of equations solved in al-Karaji's al-Badi' "likewise" appear in Leonardo of Pisa's Liber quadratorum. ⁴ In the article on the mathematical sciences, the author says that a system of linear congruences studied by Ibn al-Haytham was taken up again in the sixth/twelfth century by al-Khilati in Arabic and by Fibonacci in Latin. ⁷

The article on al-Khwarazmi describes the system of Egyptian fractions, in which a fraction is expressed as a sum of fractions whose numerator is one, and says it was developed in ancient and mediaeval times, partly because the inheritance rules of Islamic law called for exact fractional arithmetic. It says that, fully developed, the system was introduced into Europe through various Spanish versions and through Fibonacci. ³

In the article on measurement (misaha), the author writes that Leonardo's Practica geometriae remained a standard work for three centuries and depended closely on Savasorda, whose Liber embadorum shows striking similarities to a Liber mensurationis ascribed to Abu Bakr. ⁵ The supplement article on geometry says Arabic trigonometry was already long established when Fibonacci used it around 1220 for measuring surfaces. ⁸

The Encyclopaedia says nothing about Fibonacci's years of birth and death, his family, or where he met Arabic mathematics. Its statements about his dependence are by the articles' authors, written about particular books, and the museum does not extend them to his work as a whole. Further records for the Liber abaci and his other books are still to be added.