Basic Concepts Of The Trigonometry In Qing Times

This paper accounts the basic concepts and change in Qing times' trigonometry, which covers the relevant knowledge in ancient China, the trigonometric knowledge from the West and the choice Chinese made. The ancient knowledge was subject to astronomy, the basic concepts were subject to physics and the results were mostly approximate. The trigonometric knowledge introduced from the West by late Ming and early Qing was no more than special results, they were subject to astronomy as well, the basic concepts were geometrical though. Chinese scholar's trigonometry became independent of astronomy by the First Mathematical Processing, the basic concepts evolved from physical to geometrical and the approximate results were replaced by the accurate results. There was a chance for Chinese to formalize trigonometry on his own, but the scholars in late Qing refused formalism. After the algebraic trigonometry was introduced from the West, there was no room for own development any more, they did not accomplish formalization until total westernization.