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Ornar Khayyam, the Mathmetician. By R. RASHED and B. VAHABZADEH. Persian Heritage Series, no. 40. New York: BIBLIOTHECA PERSICA PRESS, 2000. Pp. x + 268. [Distributed by Eisenbrauns, Inc., Winona Lake, Inc.]
Although the name 'Umar Khayyam is familiar in the West, mainly from a nineteenth-century translation of his Ruba'iyyat, the scientific contributions of this eleventh-century Iranian philosopher, mathematician, and poet are generally unknown. In fact, very little is known about his life. Professor Rashed is convinced that two Khayyams are indicated by the historical evidence, one the poet, and the other the mathematician. Whether two Khayyams or one, the present book enables us to assess some of the mathematician Khayyam's contributions to the world mathematics tradition. Khayyam was the first mathematician we know of to formulate a thoroughgoing geometrical approach to algebraic equations, and, as Rashed shows thoroughly in his introduction, ought to be considered the precursor of Descartes in the invention of analytic geometry.
This book is a paradox. On the one hand, the meticulous care that went into preparing helpful diagrams and mathematical notation is obvious. On the other, there are omissions and an overall confusion of presentation that leaves me agape.
Three mathematical works by Khayyam (English translations only) are presented: Treatise on Algebra (Risala fi al-jabr wa al-muqabala), Treatise...