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=Etymology of Sine= further note on sinus rectus/versus |
=Etymology of Sine= |
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: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)
: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 protruding point of the arrow shaft
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