And since we follow for the most part Leonardo Pisano, I intend to clarify now that any enunciation mentioned without the name of the author is to be attributed to Leonardo.
The general absence of accreditation was not unusual; citing sources was a practice that became common much later, and authors frequently lifted entire passages from other writers without any form of acknowledgement. Without that one reference by Pacioli, later historians might never have known of the great Pisan’s pivotal role in the birth of the modern world. Yet, Pacioli’s remark was little more than a nod to history, for a reading of the entire text shows that the author drew not from Liber abbaci itself, but from sources closer to his own time. There is no indication he had ever set eyes on a copy of Liber abbaci, let alone read it. His citation of Leonardo reflects the fact that, at the time, the Pisan was considered the main authority, whose book was the original source of all the others.
Despite the great demand for mathematics textbooks, Liber abbaci itself remained in manuscript form for centuries, and therefore inaccessible to all but the most dedicated scholars. It was not only much more scholarly and difficult to understand than many other texts, it was very long. Over time it became forgotten, as people turned to shorter, more simple, and derivative texts. That one mention in Pacioli’s Summa was the only clue to Leonardo’s pivotal role in the dramatic growth of arithmetic. It lay there, unnoticed, until the late eighteenth century, when an Italian mathematician called Pietro Cossali (1748–1815) came across it when he studied Summa in the course of researching his book Origine, transporto in Italia, primi progressi in essa dell-algebra (“Origins, Transmission to Italy, and Early Progress of Algebra There”). Intrigued by Pacioli’s brief reference to “Leonardo Pisano”, Cossali began to look for the Pisan’s manuscripts, and in due course learned from them of Leonardo’s important contribution.
In his book, published in two volumes in 1797 and 1799, which many say is the first truly professional mathematics history book written in Italy, Cossali concluded that Leonardo’s Liber abbaci was the principal conduit for the “transmission to Italy” of modern arithmetic and algebra, and that the new methods spread first from Leonardo’s hometown of Pisa through Tuscany (in particular Florence) then to the rest of Italy (most notably Venice) and eventually throughout Europe. As a result, Leonardo Pisano, famous in his lifetime then completely forgotten, became known — and famous — once again. But his legacy had come extremely close to being forever lost.
The lack of biographical details make a straight chronicle of Leonardo’s life impossible. Where and when exactly was be born? Where and when did he die? Did he marry and have children? What did he look like? (A drawing of Leonardo you can find in books and a statue of the man in Pisa are most likely artistic fictions, there being no evidence they are based on reality.) What else did he do besides mathematics? These questions all go unanswered. From a legal document, we know that his father was called Guilichmus, which translates as “William” (the variant Guilielmo is also common) and that he had a brother named Bonaccinghus. But if Leonardo’s fame and recognition in Italy during his lifetime led to any written record, it has not survived to the present day.
Thus a book about Leonardo must focus on his great contribution and his intellectual legacy. Having recognized that numbers, and in particular powerful and efficient ways to compute with them, could change the world, he set about making that happen at a time when Europe was poised for major advances in science, technology, and commercial practice. Through Liber abbaci he showed that an abstract symbolism and a collection of seemingly obscure procedures for manipulating those symbols had huge practical applications.