Neugebauer's books are a fantastic resource. I am mostly familiar with their contents. I am aware of Babylonian's contribution to positional astronomy. If I re

Neugebauer's books are a fantastic resource. I am mostly familiar with their contents. I am aware of Babylonian's contribution to positional astronomy. If I remember right, Hipparchus, considered the father of trigonometry, was familiar with Babylonian astronomy. Contemporaneous (meaning Hipparchus's times) Greek astronomy was not as accurate in comparison. However, I have missed the Fourier series that you mention or any record that shows trigonometric manipulation or working out the values of the trigonometric functions. If you have a reference I would love to read, perhaps a specific Neugebauer book. Almagest model too can be considered a crude Fourier decomposition. So I am quite keen to learn about this Fourieresque decomposition that you speak of. If ancient trigonometry interests you, you should definitely checkout Indian scholars of the middle ages. Neugebauer covers some of that in his books. Glen Van Brummelen is another good resource. Awareness of angle measurement is not yet trigonometry, that would amount to saying Euclid's Elements- I has trigonometry. Trigonometry, whether planar or spherical becomes trigonometry with the awareness of trigonometric functions, their evaluations and trigonometric identities. > > However, "the same kind of mathematics" rings dismissive. > That's on you if you read it that way; Yes I do. The 'same kind of mathematics' is too broad a brush stroke that can easily sweep away any form of mathematical originality and novelty. As a characterization it is somewhere between 'vapid' and 'not very useful'. We do agree about how mind-bogglingly sophisticated Babylonian math was. They had Algebra that the Greeks didn't, and as you noted had figured out the technique of area under the curve well before Archimedes ... another person who seems centuries ahead of his times.