# Sakabe Kōhan

**Sakabe Kōhan** (坂部 廣胖, 1759 – September 16, 1824) was a Japanese mathematician in the Edo period.^{[1]}

Sakabe served for a time in the Fire Department of the shogunate, but he resigned that position to become a *rōnin* or masterless samurai. He spent the rest of this life in study, in teaching, and in promoting mathematics education in Japan.^{[2]}

Sakabe was a student of Ajima Naonobu.^{[3]}^{[4]}

Sakabe investigated some European and Chinese works which had appeared in Japan, but his general method was later construed to be innovative, clarified and thus improved.^{[5]} Foreign influence shows itself indirectly some of his published work.^{[6]}

Sakabe's *Sampo Tenzan Shinan-roku* (*Treatise on Tenzan Algebra*) in 1810 was the first published work in Japan proposing the use of logarithmic tables. He explained that "these tables save much labor, [but] they are but little known for the reason that they have never been printed in our country."^{[7]} Sakabe's proposal would not be realized until twenty years after his death when the first extensive logarithmic table was published in 1844 by Koide Shuke.^{[8]}

In Sakabe's *Treatise on Tenzan Algebra*, mathematical problems are arranged in order from easy problems to difficult ones. The text presents a method for finding the length of a circumference and the length an arc of an ellipse. This was the first appearance of the problems pertaining to ellipses in printed books in Japan.^{[9]}

## Selected works

In a statistical overview derived from writings by and about Harry Smith Parkes, OCLC/WorldCat encompasses roughly 10+ works in 10+ publications in 1 language and 10+ library holdings.^{[10]}

- 1795 —
*Shinsen Tetsujutsu*^{[2]} - 1802 —
*Kaiujutsu-keima*(*Considerations on the theory of the polygon*)^{[2]} - 1803 —
*Rippō-eijiku*, method for finding cube root^{[4]} - 1810 —
*Tenzan Shinan-roku*(點竄指南錄) OCLC 22057236896,*Treatise on Tenzan Algebra*^{[7]} - 1812 —
*Kwanki-kodo-shōhō*, measurement of spherical arcs and trigonometrical tables^{[11]} - 1816 —
*Kairo Anshin-roku*(海路安心錄) OCLC 122810576, theory of navigation applying the spherical astronomy of the West^{[6]}

## See also

- Sangaku, the custom of presenting mathematical problems, carved in wood tablets, to the public in shinto shrines
- Soroban, a Japanese abacus
- Japanese mathematics (
*wasan*)

## Notes

- ↑ Smith, David. (1914).
, p. 208, at Google Books*A History of Japanese Mathematics,*pp. 208–213. - 1 2 3 Smith,
*p. 208.*, p. 208, at Google Books - ↑ Hatashi, T. [Hayashi Tsuruichi?] "The Conic Sections in the Old Japanese Mathematics,"
, p. 173, at Google Books*The American Mathematical Monthly,*Vol. 13, No. 10 (October 1906), pp. 173–174. - 1 2 Hayashi, Tsuruichi. (1907). "A Brief history of the Japanese Mathematics,"
, p. 120, at Google Books*Nieuw archief voor wiskunde*("New Archive of Mathematics"), pp. 120. - ↑ Smith,
*p. 213.*, p. 213, at Google Books - 1 2 Smith,
*p. 266.*, p. 266, at Google Books - 1 2 Smith,
*pp. 268–270.*, p. 268, at Google Books - ↑ Smith,
*pp. 268–270.*, p. 270, at Google Books - ↑ Hayashi,
*p. 121.*, p. 121, at Google Books - ↑ WorldCat Identities: 坂部広胖 1759-1824
- ↑ Hayashi,
*p. 122.*, p. 122, at Google Books

## References

- Endō Toshisada (1896).
*History of mathematics in Japan*(日本數學史史*Dai Nihon sūgakush*). Tōkyō: _____. OCLC 122770600 - David Eugene Smith and Yoshio Mikami. (1914).
*A History of Japanese Mathematics.*Chicago: Open Court Publishing. OCLC 1515528 – note alternate online, full-text copy at archive.org *Wiskundig Genootschap*(Mathematical Society). (1907)*Nieuw archief voor wiskunde*(New Archive of Mathematics*). Amsterdam, Swets & Zeitlinger. OCLC 5814818*