The Indian word for what we call sine was 'jyā'. The Surya-siddhanta mentions 'jyā' many many times. As does the Aryabhatiya. In contrast they mention the synonym 'jivā' only once or twice. So why was 'jiva' transliterated into Arabic rather than 'jyā'? It makes no sense; 'Jyā' is written all over these texts and 'jivā' is not. Did later Indian mathematicians perhaps use 'jivā' more often? Was it one particular Arabic translator who translated a particular Indian text which happened to use 'jivā' rather than 'jyā'?
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$\begingroup$ Already answered here and here $\endgroup$– Mauro ALLEGRANZAMay 28, 2021 at 5:55
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$\begingroup$ And also here $\endgroup$– Mauro ALLEGRANZAMay 28, 2021 at 7:37
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4$\begingroup$ Does this answer your question? What is the etymology behind sine, cosine, tangent, etc.? $\endgroup$– Alexandre EremenkoMay 28, 2021 at 19:36
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2$\begingroup$ These don't answer my question Mauro. One of your links quotes Victor Katz: 'Aryabhata frequently abbreviated this term to 'jyā' or its synonym 'jivā' ... but I've looked through a commentary of the Aryabhata by Shukla/Sharma ... and while 'jyā' is mentioned often, 'jivā' is not mentioned at all. In addition, there are only 2 references to 'jivā' (as a sine) in the commentary on the Surya Siddhanta by Burgess. So it feels like 'jivā' was a rarely used synonym ... so why did it get transliterated into Arabic over 'jyā'? Unless someone else used 'jivā' a lot ... who?! $\endgroup$– segarMay 29, 2021 at 12:49
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The unabridged Oxford English Dictionary, which is quite authentic does not trace sine to any Sanskrit words
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Etymology: < Latin sinus a bend, bay, etc.; also, the hanging fold of the upper part of a toga, the bosom of a garment, and hence used to render the synonymous Arabic jaib , applied in geometry as in sense 2. Compare French sinus, Spanish seno, Italian seno.
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However, a book by A. Bello, Origins of mathematical words: a comprehensive dictionary of Latin, Greek, and Arabic roots states the following
Regardless the sad thing nobody has ever produced even images of original documents of Sanskrit, or even the authors. So take everything as a grain of salt especially the stories on Wikipedia. I am curious to see any original source and the name of the Sanskrit speaking author who first used those words.
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2$\begingroup$ There are absolutely documents in Sanskrit detailing the development of 'sine'. Just look for the Aryabhatiya and the Surya Siddhanta. The concept of 'sine' as a half-chord started with documents such as these. For translations see: archive.org/details/Aryabhatiya-with-English-commentary archive.org/details/SuryaSiddhantaTranslation/mode/2up ... but both of these use the word 'jyā' the vast majority of the time. ... and sine came from sinus, came from jayb ... came from jiba ... came from jivā ... so which Indian writers used the synonym 'jivā' ... someone must have! $\endgroup$– segarMay 29, 2021 at 12:29