Naoyuki Ajima

A mathematician and calendar scholar in the mid-Edo period. Commonly known as Manzo, his pen name was Hakuki, and his pen name was Nanzan. He was a samurai of the Shinjo domain in Dewa (Yamagata Prefecture) with a stipend of 100 koku. He studied mathematics under Irie Masatada of the Nakanishi school and Yamaji Shizumi of the Seki school, and expanded on the mathematics of Seki Takakazu and Takebe Katahiro. He expanded the 1/2 power expansion of binomials pioneered by Takebe to the 1/n power expansion, and is also famous for inventing double integrals. He also showed originality in his research on logarithms by creating an inverse logarithm table. He compiled the contents of problems equivalent to those of the Italian Gian Francesco Malfatti (1731-1807) and wrote Sansha Sanenjutsu. He left behind outstanding achievements such as the study of Laplace expansions of determinants and repeating decimals. Indeterminate equations in number theory

He has given solutions to problems such as ay ² －bx ² ＝1. In particular, his method of using the length of a common tangent to a problem of tangents between two circles is highly regarded. He also assisted his teacher, Yamaji Nushiju, in the creation of calendars.

[Shimohira Kazuo]

"The Complete Works of Naoen Ajima, edited by Akira Hirayama et al. (1966, Fuji Junior College Publishing Division)"

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

江戸中期の数学者、暦学者。通称は万蔵、字(あざな)は伯規(はくき)、号は南山。出羽(でわ)（山形県）の新庄(しんじょう)藩士で100石をとる。中西流の入江応忠(いりえまさただ)と関流の山路主住(やまじぬしずみ)に数学を習い、関孝和(せきたかかず)や建部賢弘(たけべかたひろ)らの数学を拡張した。建部が開拓した二項式の1/2乗の展開を、1/n乗の展開にまで拡張し、また二重積分の創始も名高い。対数の研究においても、逆対数表をつくる独創性を示す。イタリアのマルファッティGian Francesco Malfatti（1731―1807）の問題に相当する内容をまとめて『三斜三円術』を著す。行列式のラプラス展開、循環小数の研究など優れた業績を残す。整数論では不定方程式

とか、ay²－bx²＝1などの問題に解答を与えている。なかでも、円と円の切触問題に、その共通切線の長さを利用するくふうは高く評価されている。なお、彼は師の山路主住の作暦の手伝いもした。

［下平和夫］

『平山諦他編『安島直円全集』（1966・富士短期大学出版部）』

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