id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_s3jefpwjnndhvf5vietzfr3bxi	Jan P Hogendijk	Sharaf al-Dīn al-Ṫūsī on the number of positive roots of cubic equations	1989	17	.pdf	application/pdf	7854	1063	91	In the second part of his Algebra, Sharaf al-Din al-T&i (l2th-century) correctly determines the number of positive roots of cubic equations in terms of the coefficients. has recently published an edition of the Algebra [al-Tiisi 19851, and he has discussed alTiisi's work in connection with 17th century and more recent mathematical methods (see literal French translation, a transcription of al-Ttisi's reasoning in modern notation, and a discussion of most of the text in terms of modern algebra and analysis. contain notes to the Arabic text and the French translation in [T2], for the reader constant term can be reduced to quadratic equations, and for each of the remaining 13 types he had given a geometrical construction of a root by means of two Al-Khayyam pointed out that the number of roots of these equations depends geometrical proofs of algorithms for approximating the roots of cubic equations.	./cache/work_s3jefpwjnndhvf5vietzfr3bxi.pdf	./txt/work_s3jefpwjnndhvf5vietzfr3bxi.txt