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Fibonacci's De practica geometrie

Leonardo Fibonacci and Barnabas Hughes (tr)

Fibonacci, Leonardo; Barnabas Hughes (tr);

Fibonacci's De practica geometrie

Springer, 2008, 408 pages  [gbook]

ISBN 0387729305, 9780387729305

topics: |  math | history


Fibonacci's work is placed in the European canon, but that his antecedents
are in the orient is often glossed over.  In this impressive work of
multi-cultural scholarship, Hughes presents a detailed analysis that places
Fibonacci's possible sources on a solid foundation.  Regarding the
translation also, he makes many points about the difficulty, ambiguity and
other issues, illustrated with examples.  In contrast, Sigler's translation
of Liber Abaci leaves the reader wondering on many issues.

Expresses mixed numbers from R to L, e.g. seven and a half is  ½ 7.  This
notation is Arabic from the Maghreb, and it reflects the Arabic method of
writing from right to left.  The attempt is to capture how Fibonacci may have
thought about processes - e.g. addition x and y and z; does not replace the
and with a plus; this would be infusing modern semantics of "+" - and would
change the thinking from where everything gets combined with the lead group.

De practica geometrie (practical geometry) is Fibonacci's selections of the
most useful parts of Graeco-Arabic geometry.  It was intended for
land-measurers, surveyors, and other artisans, and complements Liber abaci.
Uses Pisan units of measure, enables finding square and cube roots,
dimensions of rectilinear and curved surfaces and solids, and analyses of
pentagons and decagons.

Did Fibonacci know Arabic?


Presents what is the consensus view today, that Fibonacci knew
arabic, and used arabic sources extensively in his work.  [after 2 pages of
analysis of Fibonacci's possible sources, concludes that he consulted an
Arab edition of Euclid's elements, and only later perhaps he looked up the
existing Latin texts and some greek terms.  This is because, based on
careful work by Menso Folkerts, there do not seem to be much agreement
between his writings and contemporary Latin texts.  Mentions work by
Allard, who originally thought F did not know Arabic, but later amended
himself.  also cites Busard 87, Rasheed, and others.

"the issue is no longer moot: Fibonacci was proficient in Arabic.  ...
[That Fibonacci] had complete fluency in Arabic, is now accepted as correct..."

   My father was a notary for Pisan merchants doing business with the customs
   office in Bougie.  He sent for me when I was a youth, with an eye to being
   useful to him now and in the future. He enrolled me in an abacus school
   for some time where I was taught to compute; a wonderful teacher
   instructed me in the art of the nine Indian digits.  I was so delighted
   with this knowledge that I preferred it to all other subjects.  In fact,
   as I journeyed about Egypt, Syria, Greece, Italy and the Provence on
   business, I studied whatever I could about this multifaceted subject, even
   discussing it with others. Liber Abaci 1.24-33 (p.xx,xxii)

the Almohad empire, with its capital in Marrakech, ruled part of Spain and
almost all Maghreb.  During this time, the six cities of
Seville (al-Andalus, Spain), Ceuta and Marrakesh (Morocco)
Tlemcen and Bougie (Algeria), and Tunis experienced men of science, teachers
and students (religion, law, mathematics, medicine...) moving back and
forth.  [cites many scholars who moved between cities, incl. the Andalusian
al-Quarashi who worked in Seville and Bougie where he died in 1184].  All
these dates makes one conjecture that the works of these eminent authors of
mathematics were circulating among the scholars of these six cities. p. xxi

Sources

Which books were used in Fibonacci's instruction, which he presumably started
around 1180
(a treaty was signed between the commune of Pisa and the Caliph, Almohad in
1186, but possibly Fi joined his father some six to eight years
earlier. p. xix)
Any one of these books might possibly been the one he studied:

* Kitab al-jam 'wal tafriq bi hisAb al-Hind (Book of Hindu reckoning) by
  al-khwArizm1.  Arabic text is lost, but med Latin translation exists
* Kitab al bayAn wa at-tudhkAr (book of demonstration and recollection) by
  al-HassAs (ca 1175)
* kitab aal-kafi fi 'ilm al-hisAb (sufficient book on the science of
  arithmetic) by al-karAji
* al-urjuza fIl-jabr wa-l muqAbala (poem on algebra) by Ibn al-Yasamin
  (d. 1204) [a concise memorabilia]
[etc]

Subsequently, during his travels, he must have collected (and have copied)
books of interest.

Gives a chapter by chapter analysis of de Practica Geometrie, to indicate
which books may have been the original influence.

traduttore tradittore (no transl given; translators are traitors? source
given as appearing in Hays 1988, p. 183)


amitabha mukerjee (mukerjee [at-symbol] gmail) 2011 Nov 07