Talk:Liber Abaci

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Wikisource link[edit]

There is a link to Liber abaci at Wikisource in the "External links". Unfortunately the book isn't actually there. If and when it does appear, the link should be replaced with {{Wikisource}}. Hairy Dude 01:28, 22 January 2007 (UTC)

"Faint idea" of place value[edit]

Since a large part of the text of Liber Abaci is devoted to explaining, in horrendous detail, the very same algorithms for arithmetic on base-10 numerals that we still employ today, I think describing its notion of place value as a "faint idea", as Milogardner did today, is not only POV, as David Eppstein said in his edit summary, but also manifestly false. Thanks for reverting. -- Dominus 09:01, 9 March 2007 (UTC)

No mention of revised edition of 1228?[edit]

I am surprised there is no elaboration of which edition appeared the Fibonacci number sequence. No mention of the dedication of Liber Abacci to Michael Scot either of 1228, nor the difference between the two editions. I have heard that the only known version is the 1228 edition. —Preceding unsigned comment added by 24.130.147.154 (talk) 07:45, 13 March 2010 (UTC)

Ed Pegg Jr: The second edition (from 1228) is essentially identical to the first edition (from 1202), with a few dedicatory paragraphs added. The Fibonacci sequence, Arabic numbers, the St Ives puzzle, and powers of 2 all appeared in the first edition, but copies of the first edition have apparently been lost to history. There are 15 copies of the second edition, but only two are complete. David Singmaster sent me some pictures taken from one of the better surviving manuscripts: [[Fibonacci sequence][1]] [[Arabic Numbers][2]]. —Preceding unsigned comment added by 140.177.205.221 (talk) 21:53, 9 August 2010 (UTC)

Justification for deleting a certain sentence[edit]

Yesterday I deleted the following sentence and another editor has asked for justification for the deletion:

In this work, Fibonacci introduced to Europe the Hindu-Arabic numerals, a major element of our decimal system, which he had learned by studying with Arabs while living in North Africa with his father, Guglielmo Bonaccio, who wished for him to become a merchant.

In relation to the above sentence, here are three points:

(1) In the Liber Abaci, there is clear evidence that Leonardo read the Algebra of Al-Khwarizmi in the Latin translation done by Gerard of Cremona, and did not read it in the Arabic of Al-Khwarizmi. Liber Abaci also copied some of its content from the Algebra of Abu Kamil, but there is no evidence that Leonardo read Abu Kamil in Arabic, and there's some evidence (not conclusive) that he read Abu Kamil in Latin translation. More more discussion about this at "The Influence of Arabic Mathematics on the Medieval West" by André Allard, in Encyclopedia of the History of Arabic Science, Volume 2 (year 1996). That book also makes the comment that Fibonacci does not use Arabic words beyond those already used by other Latin writers. He uses Arabic words that were borrowed by Gerard of Cremona (including aljebra) but he does not use Arabic words borrowed by himself. It is possible that he was fluent in Arabic, and yet refrained from borrowing Arabic words, but in any case his writings don't show that he could speak Arabic.

(2) We do not know for sure where or how Leonardo learned the Hindu-Arabic numeral system. Leonardo wrote a very short autobiography which is the main source of info about him. The following has a reproduction of the autobiography together with comments about what we can infer from it: "The Autobiography of Leonardo Pisano", by Richard E. Grimm. It is certain that Leonardo lived for a while in North Africa as a boy, and travelled to Syria and Egypt as youth or young man. But, as Richard E. Grimm says, the statements in the autobiography leave room for uncertainties. The Wikipedia article should be saying what we actually know.

(3) The deleted sentence says "Fibonacci introduced to Europe the Hindu-Arabic numerals". There are two problems with that: (1) The Arabic numeral system was already available in Latin in the later 12th century before Fibonacci wrote the Liber Abaci, and (2) Fibonacci's work did not circulate widely in the Europe of his era. The Liber Abaci is much admired today. But in Europe on the 13th century on the ground, other books were much more influential in disseminating the Arabic numerals, as evidenced by the number of surviving manuscripts. See the year 1911 book "The Hindu-Arabic Numerals", by Smith and Karpinski, chapter 7 headed "The definite introduction of the numerals into Europe" and chapter 8 headed "The spread of the numerals in Europe". The book in chapter 7 mentions by name a large handful of works on the Arabic numerals in Latin that pre-dated the Liber Abaci. It says in chapter 8 concerning the influence of the the Liber Abaci: "While not minimizing the importance of the scientific work of Leonardo of Pisa, we may note that the more popular treatises by Alexander de Villa Dei (c. 1240 a.d.) and John of Halifax (Sacrobosco, c. 1250 a.d.) were much more widely used, and doubtless contributed more to the spread of the numerals among the common people." Seanwal111111 (talk) 11:39, 15 December 2012 (UTC)