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 |
1. Introduction -- ยง1. The Beginnings of Islam -- ยง2. Islamโs 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?rโs Arithmetic -- ยง3. The Discovery of Decimal Fractions -- ยง4. Muslim Sexagesimal Arithmetic -- ยง5. Square Roots -- ยง6. Al-K?sh?โs 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 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?โs Algebra -- ยง4. Thabitโs Demonstration for Quadratic Equations -- ยง5. Ab? K?mil on Algebra -- ยง6. Al-Karaj?โs Arithmetization of Algebra -- ยง7. โUmar 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?โs Proof of the Addition Theorem for Sines -- ยง4. Nas?r al-D?nโs Proof of the Sine Law -- ยง5. Al-B?r?n?โs Measurement of the Earth -- ยง6. Trigonometric Tables: Calculation and Interpolation -- ยง7. Auxiliary Functions -- ยง8. Interpolation Procedures -- ยง9. Al-K?sh?โs 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