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Extracting Square Roots Made Easy: A Little Known Medieval Method - References

Author(s): 
Friedrich Katscher (Vienna University of Technology)

Al-Hassâr, Abû Bakr Muhammad Ibn Ayâsh (Alabuchri) (1194). Kitâb al-bayân wa al-tadkâr fi san`at `amal al-`iyar, part 1, in Arabic (digital facsimile). Manuscript number: ljs293. Philadelphia: Schoenberg Center for Electronic Text and Image, University of Pennsylvania.
http://sceti.library.upenn.edu/sceti/ljs/PageLevel/index.cfm?option=view&ManID=ljs293

Allabagh, M., & A. Djebbar (1987). “Découverte d'un écrit mathématique d'al Hassar (XII S.): Le livre I du Kamil,” Historia mathematica 14, 147-158.

Barner, Klaus (2001). “How old did Fermat become?,” NTM: International Journal for History and Ethics of Natural Sciences, Technology and Medicine (New series) 8(4), 209-228.

Barner, Klaus (2007). “Neues zu Fermats Geburtsdatum,” Mitteilungen der Deutschen Mathematiker-Vereinigung 15, 12-14.

Buteo, I. (1559). Logistica, 74-76. Lyons: Gulielmus Rovillius.

Cardano, H. (1539). Opera omnia, vol. 4 (1663): Practica arithmeticae, 30. Lyons: Ioannes Antonius Huguetan & Marcus Antonius Ravaud.

Cataldi, P. A. (1613). Trattato del modo brevissimo di trouare la radice quadra delli numeri, 12-18. Bologna: Bartolomeo Cochi.

Euler, L. (1770). Vollständige Anleitung zur Algebra. St. Petersburg: Kayserliche Academie der Wissenschaften. Many editions and translations.

Fermat, P. (1657). “Correspondance. Année 1657. LXXX. Fermat à Frénicle. Février 1657. LXXXI. Second défi de Fermat aux mathématiciens. Février 1657.” Oeuvres de Fermat, vol. 2 (1894), 333-334, 334-335. Paris: Gauthier-Villars.

Kunitzsch, P. (2007). “Al-Hassâr's Kitâb al-Bayân and the Transmission of the Hindu-Arabic Numerals.” MuslimHeritage.com (published 04 June, 2007; last accessed 10 May, 2010)
http://www.muslimheritage.com/topics/default.cfm?ArticleID=705

Lagrange, J. (1766). “Solution d'un problème d'arithmétique.” Oeuvres de Lagrange, vol. 1 (1867), 671-731. Paris: Gauthier-Villars.

Pacioli, L. (Frater Lucas de Burgo sancti Sepulchri) (1494). Summa de Arithmetica Geometria Proportioni et Proportionalita, 45 recto (paginated wrongly 46). Venice: Paganino de Paganini.

Pisano, Leonardo. (1857). Il Liber Abbaci, published by B. Boncompagni, Chapter 14. “On the finding of square and cube roots by multiplications and divisions, or on their extraction,” 353. Rome: Tipografia delle Scienze Matematiche e Fisiche.

Sigler, L. E. (2002). Fibonacci's Liber Abaci. A Translation into Modern English of Leonardo Pisano's Book of Calculation, 490-491. New York: Springer.

Suter, H. (1901). “Das Rechenbuch des Abu Zakarija el-Hassar,” Bibliotheca mathematica 2 (1901), 12-40.

Tartaglia, N. (1556). General Trattato di Numeri e Misure, vol. II, 19 verso-20 recto (wrongly paginated 25-26). Venice: Curtio Trojano dei Navo.

Whitford, E. (2008). The Pell equation (reprint of the 1912 New York, NY edition). Seaside, Oregon: Merchant Books.

Woepcke, F. (1859). “Traduction du traité d'arithmétique d'Aboûl Hasan Ali ben Mohammed Alkalçadi,” Atti dell'Accademia Pontificia de' Nuovi Lincei, vol. XII, 230-275, 399-438; “On the manner to make the approximation more exact”: 404-405.

Woepcke, F. (1874). “Intorno ad un metodo per la determinazione approssimativa degl'irrazionali di secondo grado,” Bullettino di bibliografia e di storia delle scienze matematiche e fisiche, vol. VII (1874), 255-262.

Friedrich Katscher (Vienna University of Technology), "Extracting Square Roots Made Easy: A Little Known Medieval Method - References," Convergence (November 2010), DOI:10.4169/loci003494