# Where does the word sine'' (as in $\sin x$) come from?

According to wikipedia (https://en.wikipedia.org/wiki/History_of_trigonometry) :

the modern word "sine" is derived from the Latin word sinus, which means "bay", "bosom" or "fold" is indirectly, via Indian, Persian and Arabic transmission, derived from the Greek term khordḗ "bow-string, chord".

I don't see yet why a sine is a bow-string or a chord.

• See en.wikipedia.org/wiki/Sine Wikipedia for "sine", which explanes: "The word "sine" (Latin "sinus") comes from a Latin mistranslation of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, jya-ardha.[2]" and gives a reference. – Alexandre Eremenko Feb 7 '19 at 0:42
• There is a saying that paper never refused ink. It is rather amusing to see how everything is credited to Sanskrit on the web as if Arabic mathematicians were mere translators of Greek and Sanskrit works. From the Arabs, everything was Latinized. There is a nice BBC report where it was lamented that in a recent conference, Indian scientists disproved Einstein and claimed: "... stem cell research was discovered in India thousands of years ago." Here is the link bbc.com/news/world-asia-india-46778879 – M. Farooq Feb 7 '19 at 4:28
• Possible duplicate of What is the etymology behind sine, cosine, tangent, etc.? – Carl Witthoft Feb 7 '19 at 13:36
• The Greeks never measured curves. They got hung up on st line and compass Unlike Indians who were more practical who used straight edge and string and eliminated all unrequired niceties.Indians also developed equations for differences to calculate quantities such as pi by finite differences rather than limits of infinite series. – Partha Shakkottai Jul 12 '19 at 22:47

A good researcher always double-checks multiple resources. One can never rely on one (history) source especially if it is open to editing by everyone. Wikipedia entry is quite incorrect which has nothing to with Indian, Persian transmission or Greek words. According to the unabridged Oxford Dictionary, the original definition of sine was "the length of a straight line drawn from one end of a circular arc parallel to the tangent at the other end, and terminated by the radius."

Here is the authentic 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"

• I think the point of the Wiki text is that the decision to use a Latin word meaning "bay/bend" may have been influenced by earlier use of words with same meaning to describe the sin function. – Carl Witthoft Feb 7 '19 at 18:35

https://en.wikipedia.org/wiki/Jyā,_koti-jyā_and_utkrama-jyā

defines sine and cosine, mis-translations of jya and kojya (or koti-jya) as jiba by the Arabs again mis translated to Latin "sinus" and co-sine. The sequence is jiva (Sanskrit) to jab (Arabic) to sine (bosom in Latin). The figure is here

https://en.wikipedia.org/wiki/File:Jya_and_kotijya.JPG

• We need to see the real ancient Indian texts or translations thereof to support this concept that sine and cosine are mis-translations of Sanskrit words. Wikipedia should be the last resource for addressing any serious academic question. Is there any remaining ancient Indian book which was translated into Arabic /Latin and which contained the figures, posted by Wikipedia? Even the leading unabridged dictionary (Oxford) does not trace sine to any Sanskrit word. – M. Farooq May 16 '19 at 4:13
• Of course not. It is a translation of an Arabic word (which is a mis-translation of a Sanskrit word). Aryabhata's texts may show their definitions. – Partha Shakkottai May 16 '19 at 15:41
• Is there any book of Aryabhata surviving today or everything is based on hearsay? – M. Farooq May 17 '19 at 0:55
• “Similar amusing European confusion underlies the term “surd” from the Latin surdus meaning deaf, applied today to the square root of two. That was calculated since the sulba sutra-s as the diagonal (karna) of the unit square, and the term surdus is a mistranslation of bad karna, meaning bad diagonal but misunderstood as bad ear, for the word karna also means ear." from ckraju.net/papers/Eternity-and-infinity-Pages-from-APA.pdf – Partha Shakkottai May 19 '19 at 21:57
• The above mentioned Sanskrit origin of surd is nothing but pure fiction written by a non-reliable author. Here is the accepted etymology. "< Latin surdus (in active sense) deaf, (in passive sense) silent, mute, dumb, (of sound, etc.) dull, indistinct. The mathematical sense ‘irrational’ arises from Latin surdus being used to render Greek ἄλογος (Euclid bk. x. Def.), apparently through the medium of Arabic açamm deaf, as in jaðr açamm surd root. Further see this link jeff560.tripod.com/s.html – M. Farooq May 19 '19 at 22:34