Wasan, and the development of Analysis in Japan

[EndanRinkaro]

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.

 

[haruspex]

Looks to me that page 78 gives the earliest derivation of pi in the book (using Archimedes' method, as you say). Pp 97-100 use it rather than derive it. The derivation of 22/7 on p 111 is purely heuristic, depending on the already determined (approximate) value. I didn't notice any power series forms, but I haven't looked very hard.