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Review: Innovation and Tradition in Sharaf al-Dīn al-Ṭūsī's Muʿādalāt

Reviewed Work: Sharaf al-Dīn al-Ṭūsī, oeuvres mathématiques: Algèbre et géométrie au XIIe siècle by Roshdi Rashed
Review by: J. L. Berggren , Sharaf Al-Dīn Al-Tūsī
Journal of the American Oriental Society
Vol. 110, No. 2 (Apr. - Jun., 1990), pp. 304-309
DOI: 10.2307/604533
Stable URL: http://www.jstor.org/stable/604533
Page Count: 6
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Innovation and Tradition in Sharaf al-Dīn al-Ṭūsī's Muʿādalāt
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Abstract

The largest treatise in Roshdi Rashed's edition of the mathematical works of Sharaf al-Dīn al-Ṭūsī is Al-muʿādalāt, a work devoted to the solution of cubic equations. This treatise shows that Islamic authors went considerably beyond the achievements of ʿUmar al-Khayyāmī in three areas: (1) finding conditions for the existence of solutions to cubic equations, (2) discovering algorithms for calculating these solutions, and (3) justifying these algorithms. Although so much is clear, it is still no easy task to understand Sharaf al-Dīn's thought processes and so achieve an understanding of the historical filiations of the document. Rashed has argued that Sharaf al-Dīn discovered the derivative of cubic polynomials and realized its significance for investigating conditions under which cubic equations were solvable; however, other scholars have suggested quite different explanations of Sharaf al-Dīn's thinking, which connect it with mathematics found in Euclid or Archimedes. Our purpose in the present essay review is to decide which of these three readings seems best to fit the text.

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