Content deleted Content added
No edit summary |
more comments and references on etymology |
||
Line 52:
:Note that the "versed sine" is 1–cos(&theta) = distance from the center of the chord to the center of the arc. I'm guessing that ''rectus'' and ''versus'' here refer to what we would now call the ''y'' and ''x'' coordinates, assuming that they originally drew a circle and measured the angle from the horizontal...Boyer doesn't say, however. Further evidence for this is the fact, according to the OED, that "sagitta", originally a synonym for the versed sine, is also an obsolete synonym for [[abscissa]]. ''sagitta'' is Latin for "arrow", and according to the OED's citations this is a visual metaphor for the versed sine (if you see the arc as the bow, the chord as the string, and the versed sine as the arrow shaft). Note that Wikipedia could use a short entry on [[versed sine]]. [[User:Stevenj|Steven G. Johnson]] 21:55, 25 Mar 2004 (UTC)
If you search for "jaib sinus" online, you find a number of other sources that confirm Boyer's etymology, notably:
* Eli Maor, ''[http://www.pupress.princeton.edu/books/maor/ Trigonometric Delights]'', ch. 3: "[http://www.pupress.princeton.edu/books/maor/chapter_3.pdf Six Functions Come of Age]" (Princeton Univ. Press, 1998).
* [http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Trigonometric_functions.html Trigonometric functions] (''MacTutor History of Mathematics Archive'')
* Amartya Sen, "[http://www1.timesofindia.indiatimes.com/articleshow/33808779.cms Not Frog, But Falcon]", ''The Times of India'' (Jan. 9, 2003).
* [http://www.ualr.edu/~lasmoller/trig.html The birth of trigonometry]
Some of these transliterate this Hindu term as ''jya'' instead of ''jiva''. Maor attributes the first translation to Gherardo of Cremona (c. 1150) instead of Robert of Chester. Boyer, however, describes how both Robert of Chester and Gherardo of Cremona, along with several others, were contemporaries who were gathered together in Toledo by the archbishop there, where a school of translation was developed. Boyer says that Robert made the first translation of e.g. the Koran and of al-Khwarizmi's ''Algebra'', among other things. Boyer also says, however, that most of these works are not dated, so it is possible that there is some uncertainty over who first translated the trigonometric work.
Maor also says that, although the first use of half-chords was in the ''Siddhanta'', the first explicit reference to the sine function was the ''Aryabhatiya'' a century later. There, Aryabhata the elder uses the term ''ardha-jya'', which means "half-chord", which he later shortens to ''jya'' or ''jiva''.
Some of these online works, especially the Maor book, seem quite nice. It would be great if some of this information could make its way into Wikipedia. [[User:Stevenj|—Steven G. Johnson]] 02:48, Mar 26, 2004 (UTC)
| |||