Author	Berggren, J. L. author
Title	Episodes in the Mathematics of Medieval Islam [electronic resource] / by J. L. Berggren
Imprint	New York, NY : Springer New York, 1986
Connect to	http://dx.doi.org/10.1007/978-1-4612-4608-4
Descript	XIV, 197 p. 18 illus. online resource

From the reviews: The book is, in spite of the author's more modest claims, an introductory survey of main developments in those disciplines which were particularly important in Medieval Islamic mathematics...No knowledge of mathematics (or of the history of mathematics) beyond normal high-school level is presupposed, and everything required beyond that (be it Apollonian theory of conics or the definitions of celestial circles) is explained carefully and clearly. Scattered throughout the work are a number of lucid remarks on the character of Islamic mathematics or of mathematical work in general. The book will hence not only be an excellent textbook for the teaching of the history of mathematics but also for the liberal art aspect of mathematics teaching in general. - Jens Hรธyrup, Mathematical Reviews ...as a textbook, this work is highly commendable...It is definitely the product of a skillful mathematician who has collected over the years a reasonably large number of interesting problems from medieval Arabic mathematics. None of them is pursued to exhaustion, but all of them arranged in such a way, together with accompanying exercises, so that they would engage an active mind and introduce a subject, which I am sure the author agrees with me is, at this stage, very difficult to introduce. - G.Saliba, Zentralblatt

1. Introduction -- ยง1. The Beginnings of Islam -- ยง2. Islamโ{128}{153}s Reception of Foreign Science -- ยง3. Four Muslim Scientists -- ยง4. The Sources -- ยง5. The Arabic Language and Arabic Names -- Exercises -- 2. Islamic Arithmetic -- ยง1. The Decimal System -- ยง2. K?shy?rโ{128}{153}s Arithmetic -- ยง3. The Discovery of Decimal Fractions -- ยง4. Muslim Sexagesimal Arithmetic -- ยง5. Square Roots -- ยง6. Al-K?sh?โ{128}{153}s Extraction of a Fifth Root -- ยง7. The Islamic Dimension: Problems of Inheritance -- Exercises -- 3. Geometrical Constructions in the Islamic World -- ยง1. Euclidean Constructions -- ยง2. Greek Sources for Islamic Geometry -- ยง3. Apolloniosโ{128}{153} Theory of the Conics -- ยง4. Ab? Sahl on the Regular Heptagon -- ยง5. The Construction of the Regular Nonagon -- ยง6. Construction of the Conic Sections -- ยง7. The Islamic Dimension: Geometry with a Rusty Compass -- Exercises -- 4. Algebra in Islam -- ยง1. Problems About Unknown Quantities -- ยง2. Sources of Islamic Algebra -- ยง3. Al-Khw?rizm?โ{128}{153}s Algebra -- ยง4. Thabitโ{128}{153}s Demonstration for Quadratic Equations -- ยง5. Ab? K?mil on Algebra -- ยง6. Al-Karaj?โ{128}{153}s Arithmetization of Algebra -- ยง7. โ{128}{152}Umar al-Khayy?m? and the Cubic Equation -- ยง8. The Islamic Dimension: The Algebra of Legacies -- Exercises -- 5. Trigonometry in the Islamic World -- ยง1. Ancient Background: The Table of Chords and the Sine -- ยง2. The Introduction of the Six Trigonometric Functions -- ยง3. Abu l-Waf?โ{128}{153}s Proof of the Addition Theorem for Sines -- ยง4. Nas?r al-D?nโ{128}{153}s Proof of the Sine Law -- ยง5. Al-B?r?n?โ{128}{153}s Measurement of the Earth -- ยง6. Trigonometric Tables: Calculation and Interpolation -- ยง7. Auxiliary Functions -- ยง8. Interpolation Procedures -- ยง9. Al-K?sh?โ{128}{153}s Approximation to Sin(1ยฐ) -- Exercises -- 6. Spherics in the Islamic World -- ยง1. The Ancient Background -- ยง2. Important Circles on the Celestial Sphere -- ยง3. The Rising Times of the Zodiacal Signs -- ยง4. Stereographic Projection and the Astrolabe -- ยง5. Telling Time by Sun and Stars -- ยง6. Spherical Trigonometry in Islam -- ยง7. Tables for Spherical Astronomy -- ยง8. The Islamic Dimension: The Direction of Prayer -- Exercises