History Of Geometry

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theorem for solving spherical triangles, as well, and for several centuries his trigonometry was the primary introduction to the subject for any astronomer. At perhaps the same time as Ptolemy, however, Indian astronomers had developed a trigonometric system based on the sine function rather than the chord function of the Greeks. This sine function, unlike the modern one, was not a ratio but simply the length of the side opposite the angle in a right triangle of fixed hypotenuse. The Indians used various values for the hypotenuse.
Late in the 8th century, Muslim astronomers inherited both the Greek and the Indian traditions, but they seem to have preferred the sine function. By the end of the 10th century they had completed the sine and the five other functions and had discovered and proved several basic theorems of trigonometry for both plane and spherical triangles. Several mathematicians suggested using r = 1 instead of r = 60; this exactly produces the modern values of the ...

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