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The Almaudia and Astronomy
Talmi made many of his calculations with something called the theorem of menolias, which is much less efficient than trig functions. So Tousi by about 13th century said, why do we need to do that? We have now fresh trigonometric functions that are simpler to use, easier to tabulate. It was through interactions like this with the almaudia that make it so scientifically valuable. New methods for astronomy and new methods for mathematics.