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.
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
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)