Takebe Katahiro was born in 1664 at Edo (now Tokyo). His father, Takebe Naotsune, was a Yuhitsu (secretary) of the Shogun. In 1676, when he was 13 years old, he and his elder brother Takebe Kataaki (1661–1716) became pupils of SEKI Kowa (d. 1708) and studied mathematics. The Takebe brothers and Seki Kowa were colleagues in the Shogun's government, and their families were the same rank: 300 koku. 1
Takebe's mathematical works are in three fields. One concerns completing the tenzan‐jutsu or endan‐jutsu (lit. addition and subtraction methods, Japanese algebra system), which was created by Seki Kowa. In the second work Takebe created the tetsu‐jutsu (inductive methods). Using these methods he obtained the formula of (arcsin θ) 2. In the third, for computing the approximate value of fractions, he solved the Diophanine equations using the reiyaku‐jutsu (continual division method). Takebe also worked in astronomy and geography.
In 1683, Takebe wrote his first work, Kenki Sampo(Studies for...
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