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arXiv · 0912.1130

Aspects Analytiques Dans la Mathematique De Sharaf Al-Dîn Al-TÛSÎ

Nicolas Fares
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Abstract

The analytical aspects of the "Traité des équations" of Sharaf al-Dîn al-Tûsî (2nd half of the XIIth century) have been underlined by R. Rashed (1974, 1986). In the present paper, we consider again some of those aspects, when studying the "second part" of the "Traité". We find out that al-Tûsî introduces certain notions, develops reasonings and uses calculating procedures that may allow his work to be an important reference in the history of the mathematical analysis. As such, one is led to examine the foundations of a J.P. Hogendijk conjecture (1989), which situates the advanced mathematics of this "2nd Part" in the only domain of Euclidian geometry. Simultaneously, we shall try to shed some light on a passage of the "Traité", made unclear by al-Tûsî style and expression. Our study is essentially based on the texts to confirm the originality and the importance of these XIIth century mathematics. I would like to express my thanks to Prof. C. Houzel (Univ. Paris VII) and B. El-Mabsout (Univ. Paris VI), for reading the manuscript and providing their precious remarks.

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Nicolas Fares. 2009-12-06. Aspects Analytiques Dans la Mathematique De Sharaf Al-Dîn Al-TÛSÎ. https://arxiv.org/abs/0912.1130

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