Abstract
The branch of elementary mathematics whose origins most clearly lie in astronomy is trigonometry, for there is no trace of this subject until Hellenistic astronomers devised geometrical models for the motion of the sun , moon, and five known planets required calculating the values of certain sides and angles of a triangle from other, given, ones. Astronomers of ancient India also used the Greek models and therefore faced the same mathematical problems, and it is the astronomical handbooks, or commentaries on them, by Greek and Indian authors, that furnish most of our record of the early history of trigonometry.
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Notes
- 1.
The Arabic word qaus can mean either ‘arc’ or ‘bow’, depending on the context.
- 2.
Adelard of Bath, in the early twelfth century. translated into Latin the reworking of these tables and rules for their use by the Cordovan astronomer Maslama of Madrid, who died in 1070 A.D. We have used the English translation of that text in Neugebauer (1962).
- 3.
He was, therefore, roughly a contemporary of another great mathematician and astronomer, Naṣīr al-Dīn al Ṭūsī, whose work we discuss elsewhere in this chapter and who worked at the eastern end of the Islamic world.
- 4.
For an account of Ptolemy’s procedure see Aaboe, A. 1997.
- 5.
This probably refers to geometrical constructions rather than by calculations using tables.
- 6.
The difference between the value of a Sine shown this short table and the value in a modern sine table (normalized to a unit radius) is never more than .002.
- 7.
See Sédillot and Sédillot, pp. 347–348.
Bibliography
Aaboe, A. 1954. “Al-Kāshī’s Iteration Method for Sin(l)”. Scripta Mathematica 20: 24–29.
Aaboe, A. Episodes from the Early History of Mathematics. The Mathematical Association of America,1997. Hamadanizadeh, J. “A Survey of Medieval Islamic Interpolation Schemes”. In: From Deferent to Equant: A Volume of Studies of the History of Science in the Ancient and Medieval Near East, Dedicated to E. S. Kennedy. (King, D. A. and G. A. Saliba, eds.). New York: New York Academy of Sciences. 1987, pp. 143 – 152.
King, D. A. The Astronomical Works of Ibn Yūnus. (Unpublished Yale Ph.D. thesis.) New Haven: Yale University, 1972.
Neugebauer, O. 1962. The Astronomical Tables of al-Khwarizmi. Copenhagen: Dansk Videnskabernes Selskab 4: 2.
Rosenfeld, B. and J. P. Hogendijk. “A Mathematical Treatise Written in the Samarqand Observatory of Ulugh Beg.” Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften. 13 (2002/2003), 25 – 65.
Sédillot, J.-J. and L.-A, Sēdillot. Traité des instruments astronomiques des Arabes. Reprinted by Institut für die Geschichte der arabisch-islamischen Wissenschaften. Frankfurt a.M., 1984.
al-Ṭūsī, Naṣīr al-Dīn (transl. by C. Caratheodory). Traité du Quadrilatère. Constantinople: 1891.
Van Brummelen, Glen. The Mathematics of the Heavens and the Earth: The Early History of Trigonometry. Princeton, New Jersey: Princeton University Press, 2009.
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Berggren, J.L. (2016). Trigonometry in the Islamic World. In: Episodes in the Mathematics of Medieval Islam. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3780-6_5
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