The Etymology of “Sine”


The English word “sine” comes from a series of mistranslations of the Sanskrit jya-ardha (chord half). Aryabhata frequently abbreviated this term to jya or jiva. When some of the Hindu works were later translated into Arabic, the word was simply transcribed phonetically into an otherwise meaningless Arabic word jiba. But since Arabic is written without vowels, later writers interpreted the consonants jb as jaib, which means bosom or breast. In the twelfth century, when an Arabic trigonometry work was translated into Latin, the translator used the equivalent Latin word sinus, which also meant bosom, and by extension, fold (as in a toga over a breast) or a bay or gulf. This Latin word has now become our English “sine”.


When Alfonso VI of Castile (Spain) captured Toledo from the Moors in 1085, he did not burn their libraries, containing a wealth of Muslim manuscripts. Under the encouragement of the Archbishop of Toledo, a veritable intelligence evaluation center was set up. A large number of translators, the best know of whom was Gerard of Cremona (1114-1187), translated from Arabic, Greek and Hebrew into Latin, at last acquainting Europe not only with classical Greek mathematics, but also with contemporary Arab algebra, trigonometry and astronomy. ...

When Robert of Chester, one of the Toledo translators, translated al-Khowarizimi's Algebra from Arabic into Latin in 1145, he encountered this word (jb) without knowing its Hindu origin; supplying the missing vowels, he found the word for bay or inlet, and the Latin for bay, inlet or cavity is sinus.


The jya of Aryabhata found its way into the works of Brahmagupta as kramajya. This was changed to karaja when it went over into Arabic, and as such appears in the Bagdad School of the 9th century. In particular, al-Khowarizmi used it in the extracts which he made from the Brahmasiddhanta of Brahmagupta, probably the work known as the Sindhind. ... The sine also appears in the Panca Siddhantika of Varahamihira (c. 505), where a table is computed with the Greek diameter of 120. Indeed, the probability of Greek influence upon the methods used by the Hindu's is very strong.

The Arabs used the meaningless word jiba, phonetically derived from the Hindu jya. The consonants of the word permitted the reading jaib, which means bosom, and so this was adopted by later Arabic writers.

When Gherardo of Cremona (c. 1150) made his translations from the Arabic he used sinus for jaib, each word meaning a fold [footnote: Jaib means bosom, breast, bay; and sinus means bosom, bay, a curve, the fold of the toga about the breast, the land about a gulf, a fold in land] and this usage, possibly begun even earlier, was followed by other European scholars.

- Smith, History of Mathematics, vol. II, pg. 616