I would like to talk about Hipparchus and Trigonometry. Before that Surya Siddhanta contains chord tables. Aryabhatta composed, there should be only one ‘t’ over here, I apologize, it is a mistake, composed sign tables in 3.5° segments the Gian sine and cosine. Pingala and Chandasastra in 400 BCE worked on combinatorics and binomials. Vriddhigarga 500 BCE, he proposed precession of Equinox. He said 1° for 100 years the same thing I said 25,500 years. Vriddhigarga had proposed it as 36,000 years. So very strong schools of propositional logic among Jains, Sanskrit scholars and Vedanta and this knowledge transmission route is via Aristotle and Alexandria. Hipparchus who lived between 190 and 120 BCE worked on chord tables in 7.5° segments. He proposed the same rate of precession as Vriddhigarag as 36,000 years. Plutarch shows that Hipparchus was able to do something called enumerative combinatorics which Pingala had already done a long time ago. Same thing as Pingala’s work. This propositional logic is in stoicism and stoicism is an offshoot of Plato. It is rooted in thoughts of Vedanta, Brahman and so on. So once again you see echoes of Indic thought in Hipparchus. The western position is that Hipparchus thought his astronomy, sorry, trignometry to the Indians. So Aryabhatta learn this Trigonometry from the works of Hipparchus. That is the statement.
Ptolemy is also supposed to be one of the sources for Aryabhatta’s work and in this book by Robert Newton, he says that every observation of Ptolemy was allegedly fabricated. He alleges that Ptolemy was liar and a plagiarist, and he suggests that the Trigonometric tables calculated by him were actually done by Eratosthenes of Egypt. So, we need to understand who this Eratosthenes is? Eratosthenes is this person who is a mathematician, astronomer, geographer, poet, music theorist and his day job was he was a chief librarian at Alexandria. He had a lot of time on his hands to read manuscripts from India and learn a lot about India and what’s going on. So library at Alexandria, well before that, he worked on the circumference of the earth, tilt of earth’s axis, distance from earth to sun, measure of the diameter of the sun, diameter of the earth, same thing Yajnavalkya had done in 3000 BCE, same thing. He worked on Stoicism of Plato. This library was destroyed by Julius Ceaser in 40 BCE and then by the Pope when Europe became Christian in 341 current era to stamp out all of Pagan works. Destroyed by the Muslims in 690 CE current era and this library essentially facilitated sourcing knowledge from the east and transmitting it to the west.
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