Hirotaka Sakabe - Hirotaka Sakabe

Japanese: 坂部広胖 - さかべ・こうはん

Year of death: 24th August 1824 (16th September 1824)
Year of birth: 1759
A Japanese mathematician in the late Edo period. Commonly known as Yuzaemon, his pen names were Shiken, Nakagaku, or Kansui, and he was also known as Banseido. He initially took the surname Toda, later changing back to Sakabe and then to Toda. He studied Japanese mathematics under Honda Toshiaki, and later became a disciple of Ajima Naoen, receiving Kaiden. He was a disciple of the Seki school (the fifth generation of Seki Takakazu's disciples). He was a fire brigade officer for the shogunate, but later became a ronin and taught mathematics exclusively. He wrote the 15-volume Sanpo Tenkan Shinanroku in 1810, and the 115th problem in the book deals with an ellipse inscribed in a rectangle. Although it is not in the form of a theorem, it shows that in modern terms, (length of the diagonal)2=(major axis of the ellipse)2+(minor axis of the ellipse)2. In Europe, this is said to have been a result obtained by P. de La Hire of France in 1704. This is a little-known question, but the results are impressive.

(Yoshimasa Michiwaki)

Source: Asahi Japanese Historical Biography: Asahi Shimbun Publications Inc. About Asahi Japanese Historical Biography

Japanese:

没年：文政7.8.24(1824.9.16)
生年：宝暦9(1759)
江戸後期の和算家。通称勇左衛門,字は子顕,中岳または澗水,また晩成堂とも号した。初め戸田姓を名乗り,のち坂部,さらに戸田にかえった。和算を本多利明に学び,のち安島直円の門に入り,皆伝を受ける。関流五伝(関孝和の弟子の5代目)。幕府の火消与力であったが,のち浪人となり専ら数学を教授した。『算法点竄指南録』全15巻を文化7(1810)年に著し,その第百十五題は矩形(長方形)に内接する楕円を取り扱い,定理という形ではないが現代風に表すと(対角線の長さ)2=(楕円の長径)2+(楕円の短径)2を示した。これはヨーロッパでは1704年にフランスのラ・イール(P.de La Hire)の得た結果といわれる。本問は余り知られていないが,素晴らしい結果である。

(道脇義正)

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