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=Etymology of Sine= |
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<br>—[[User:Herbee|Herbee]] 20:56, 2004 Mar 25 (UTC)
:It's not that Webster is wrong, per se—the English "sine" does come from ''sinus''—but the reason why ''sinus'' was used is apparently much more interesting than you assume. My source is Carl B. Boyer, ''A History of Mathematics'', 2nd ed. (see references). He writes (p. 209):
::...Thus was born, apparently in India, the predecessor of the modern trigonometric function known as the sine of an angle; and the introduction of the sine function represents the chief contribution of the ''Siddhantas'' to the history of mathematics. Although it is generally assumed that the change from the whole chord to the half chord took place in India, it has been suggested by Paul Tannery, the leading historian of science at the turn of the century, that this transformation of trigonometry may have occurred at Alexandria during the post-Ptolemaic period. Whether or not this suggestion has merit, there is no doubt that it was through the Hindus, and not the Greeks, that our use of the half chord has been derived; and our word "sine," through misadventure in translation (see below), has descended from the Hindu name, ''jiva''.
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:(Note that the "versed sine" is 1–cos(&theta). 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.) [[User:Stevenj|Steven G. Johnson]] 21:55, 25 Mar 2004 (UTC)
:By the way, assuming an etymology of ''sinus'' for sine because of the "curvaceous shape" of the sine (from the other meaning of ''sinus'' for "curve," in particular the curved shape of a draped toga or garment) is probably an anachronism. Plots of the sine function ala analytic geometry didn't come until centuries after Chester. On the other hand, Chester may have mistakenly thought that "bay" alluded to the subtended arc; I'm just speculating, though. [[User:Stevenj|Steven G. Johnson]] 22:18, 25 Mar 2004 (UTC)
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