The Scroll of Heaven and Earth

Japanese: 乾坤之巻 - けんこんのまき

A book that explains how to make a formula equivalent to the power series expansion of (arcsin x ) ^2. It was written around 1750, but the author is unknown. It is also called "Enri Kenkon no Maki." Infinite series expansion in the Edo period began with Takebe Katahiro. Takebe announced the series expansion of (arcsin x ) ² and the binomial series with exponent 1/2 around 1720. This book is a re-organization of these, and had a great influence on later Japanese mathematicians. Let A be the midpoint of the minor arc BC = s of a circle with diameter d . Let BC = a and the height (arrow) of the bow BAC be h (Figure).

Source: Heibonsha World Encyclopedia, 2nd Edition Information

Japanese:

(arcsinx)²のべき級数展開に相当する公式の作り方を解説した書。1750年ごろの著作だが著者は不明。《円理乾坤之巻》ともいう。江戸時代の無限級数展開は建部賢弘から始まる。建部は(arcsinx)²の級数展開および指数1/2の二項級数を1720年ごろ発表した。これらをまとめ直したのが本書で，後の和算家に大きな影響を与えた。直径dの円の劣弧BC＝sの中点をAとする。BC＝a，弓形BACの高さ(矢)をhとする(図)。

出典　株式会社平凡社世界大百科事典第２版について　情報

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