Sakabe served for a time in the Fire Department of the shogunate, but he resigned that position to become a ronin or masterless samurai. He spent the rest of this life in study, in teaching, and in promoting mathematics education in Japan.
Sakabe investigated some European and Chinese works which had appeared in Japan, but his general a method was later construed to be innovative, clarified and thus improved. Foreign influence shows itself indirectly some of his published work.
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." 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 Shuki.
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.
- 1795 — Shinsen Tetsujutsu
- 1802 — Kaiujutsu-keima (Considerations on the theory of the polygon)
- 1803 — Rippō-eijiku, method for finding cube root
- 1810 — Tenzan Shinan-roku (點竄指南錄?) OCLC 22057236896, Treatise on Tenzan Algebra
- 1812 — Kwanki-kodo-shōhō, measurement of spherical arcs and trigonometrical tables
- 1816 — Kairo Anshin-roku (海路安心錄?) OCLC 122810576, theory of navigation applying the spherical astronomy of the West
- Sangaku, the custom of presenting mathematical problems, carved in wood tablets, to the public in shinto shrines
- Soroban, a Japanese abacus
- Japanese mathematics (wasan)
- Smith, David. (1914). A History of Japanese Mathematics, pp. 208–213. , p. 208, at Google Books
- Smith, p. 208. , p. 208, at Google Books
- Hatashi, T. [Hayashi Tsuruichi?] "The Conic Sections in the Old Japanese Mathematics," The American Mathematical Monthly, Vol. 13, No. 10 (October 1906), pp. 173–174., p. 173, at Google Books
- Hayashi, Tsuruichi. (1907). "A Brief history of the Japanese Mathematics," Nieuw archief voor wiskunde ("New Archive of Mathematics"), pp. 120., p. 120, at Google Books
- Smith, p. 213. , p. 213, at Google Books
- Smith, p. 266. , p. 266, at Google Books
- 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
- 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