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subsequent chapters. Rather, the key was Liber Abaci’s positional arithmetic, which boiled down to positional methods of arithmetical operations, vastly easier than the non-positional Roman arithmetic. It was this positional arithmetic that paved the way for the upcoming
Commercial Revolution. Fibonacci seized the crown legacy of the Islamic Golden Age which was about to end. The Indian numeral shapes were an accident of history and could have been replaced by any set of 10 characters. Below is an example of such a replacement that predated Liber Abaci and was transformative.
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15. Sefer ha-Mispar had its own impact on commerce and finance, earlier than did Liber Abaci and in a different language and community, yet in the same area – Europe. Eventually, printing in vernaculars spread the legacy of Liber Abaci into the community of Sefer ha-Mispar which was promptly forgotten. Its only printed edition has been a modern research book on math history, bilingual Hebrew – German, 1895 Frankfurt, available on Amazon, Sefer ha-Mispar by
Abraham ibn Ezra – Das Buch der Zahl, $ 17, printed from digitized Google Books.
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593:: "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."
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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
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Sefer ha-Mispar has the following chapters: Introduction (of the positional system), Multiplication, Division, Addition, Subtraction, Fractions, Proportions (including problems from commerce), Roots. It is about 20 times shorter than Liber Abaci and has 11 extant copies compared to Liber Abaci’s
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It is important to clarify what the historical significance of Liber Abaci was. It was NOT the introduction of Hindu-Arabic numeral shapes, since any other shapes would do the job too. Nor was it in the positional notations, which is only the first step in the book and of little use without the
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meaning doesn't work. And if you think that the adjective modifies something other than the abacus, then first where is that other thing and second why is abacus nominative or genitive when it should be accusative or ablative and probably also have a preposition? That translation is as bad as the
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Not in Latin. In Latin, the adjective meaning free is also "liber" (in the masculine singular nominative form) but it could only be used in that form with a masculine singular nominative noun. "Abaci" is genitive singular or maybe nominative plural, but in either case it doesn't match and that
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There is some history given on the title of the book, and it's relation to the works content or even intent. Before reaching this paragraph, I had roughly translated the title as 'Free of the Abacus' and after reading the paragraph on the titles translation I feel that mine is more fitting.
569:. 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 Knowledge article should be saying what we actually know.
565:(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:
585:", 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
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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
572:(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
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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
562:) 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.
558:(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
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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
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Furthermore, the title being a declaration of freedom from the abacus seems intuitively correct...a mathematician saying "here is the future of mathematics,leave your abaci behind!" ~~wahoo401@yahoo~~
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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:
542:, 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.
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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
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Page 2 of Sefer ha-Mispar written by Ibn Ezra in Hebrew around 1146 says: “Wise men of India gave shapes to nine numerals which are:
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either of 1228, nor the difference between the two editions. I have heard that the only known version is the 1228 edition.
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P.S. I apologize for accidentally deleting the rest of the talk page. Could somebody please help me restore it. Thanks.
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Sorry, but that's not what "liber" means in this context. And the case of abaci is wrong for that meaning. —
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Yesterday I deleted the following sentence and another editor has asked for justification for the deletion:
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on
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But instead of these shapes I will write (the numeral shapes known to the reader):
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said in his edit summary, but also manifestly false. Thanks for reverting. --
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with his father, Guglielmo
Bonaccio, who wished for him to become a merchant.
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and also the shape of a circle O for the numeral of the value of none.”
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It might be a nice idea to mention that this is a book in Latin, right?
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In my language, it *can* be used as an adjective in *this* exact sense!
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I am surprised there is no elaboration of which edition appeared the
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9, 8, 7, 6, 5, 4, 3, 2, 1 (shown here in a modern font).
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sequence. No mention of the dedication of Liber Abacci to
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In relation to the above sentence, here are three points:
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Encyclopedia of the
History of Arabic Science, Volume 2
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In this work, Fibonacci introduced to Europe the Hindu-
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Meaning 'book', can also mean the adjective 'free'.
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