Trigonometry offers one of the most remarkable examples of transmission of the exact sciences in antiquity and the Middle Ages. Originating in Greece, it was transmitted to India and, with several modifications, passed into the Islamic world. After further development it found its way to medieval Europe.
The very term “sine” illustrates the process of transmission. The Greek word for “chord” (εύθεîα, literally “a straight line [subtending an arc]”) was translated into Sanskrit as jīva or jyā (“string of a bow”) from the similarity of its appearance. The former word was phonetically translated into Arabic as jyb, which was vocalized as jayb (meaning “fold” in Arabic), and this was again translated into Latin as sinus, an equivalent to the English sine.
It was by tracking back along this stream of transmission that the first chord table ascribed to Hipparchus (fl. 150 BCE) was recovered by Toomer (1973) from an Indian sine table (compare Tables 1 and 2). Toomer showed that some...
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References
Gupta, R. C. South Indian Achievements in Medieval Mathematics. Gaṇita‐Bhāratī 9.1–4 (1987): 15–40.
Hayashi, Takao. Āryabhaṭa's Rule and Table for Sine‐Differences. Historia Mathematica 24 (1997): 396–406.
Pingree, David and David Gold. A Hitherto Unknown Sanskrit Work Concerning Mādhava's Derivation of the Power Series for Sine and Cosine. Historia Scientiarum 42 (1991): 49–65.
Toomer, Gerald J. The Chord Table of Hipparchus and the Early History of Greek Trigonometry. Centaurus 18 (1973): 6–28.
‐‐‐. Ptolemy's Almagest. New York: Springer Verlag, 1984.
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Yano, M. (2008). Trigonometry in Indian Mathematics. In: Selin, H. (eds) Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4425-0_9299
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