I am writing an article on the development of Japanese mathematics during Japan's Sakoku, (closed from the world) period. While going through a book (http://2020ok.com/books/42/a-history-of-japanese-mathematics-41542.htm), I came to know about how Seki Kowa, and then later Takebe, developed what is known as the Yenri, (Circle Principle). I would be extremely glad if some people would give me more inputs on Yenri that what is there in the book. As far as I can tell, Yenri uses Archimedes' method of determining the value of pi by polygonal methods, and by converging fractions series. Please look at the pages 97-100, and 108 to 112. Surely, certain equations given there must have some logical derivations!! Please tell me what more to add, as this is a technical article, and I don't want to mess up historical facts.