Inheritance of the title - Idaikeisho

This is one of the question-and-answer formats in mathematics (wasan) from the Edo period. Jingoki, published in 1641 (Kan'ei 18), contains 12 questions to test the reader's ability. In the preface, the author, Yoshida Mitsuyoshi, says that at that time, many people opened mathematics private schools despite not having any mathematical ability, and that these 12 questions were intended to test the ability of the teachers at those schools. Such questions written in mathematics books are called 'Idai'. Twelve years later, Enami Tomosumi was the first to present the solutions to the Idai questions in Jingoki in his book 'Sanryoroku'. Eight new Idai questions were submitted to Sanryoroku, and this marked the beginning of a relay-style question-and-answer system known as Idai-kei. Idai-kei, which began with Jingoki, became a big hit, and many mathematics books were published that included the solutions to the Idai questions from the previous author along with the author's own questions. The number of posthumous questions also increased to 100 or 150, and some books contained only the answers to the former questions and the questions posed by the author himself. The content of mathematics rapidly became more advanced, and by the end of the 17th century, advanced mathematics such as determinants, higher-order equations, and indeterminate equations had begun to be studied. Endo Toshisada classifies the lineage of posthumous questions into the first series beginning with Jinkoki, the second series beginning with Suugaku no Mutsu Jiu Orai, Suanpo Futsudan Kai, and Suanpo Shodan Shu, the third series beginning with Suugaku no Mutsu Jiu Orai, the fourth series beginning with Suanpo Futsudan Kai, and Suanpo Shodan Shu, respectively. However, it was only the first series that actually had a major impact on later generations, and in particular the tenth question in Jinkoki, "Circle Cut Product," provided the impetus for the development of infinite series in the early 18th century. It can be said that Seki Takakazu and Takebe Katahiro achieved success as mathematicians through the first system.

[Shimohira Kazuo]

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

江戸時代の数学（和算）の問答形式の一つ。1641年（寛永18）刊の『塵劫記(じんごうき)』には、読者の力試しの問題12問がある。著者の吉田光由(みつよし)は序文のなかで、その当時、数学の力がないのに数学塾を開いている者が多かったとし、この12問は、塾の先生の力量を試すための問題だといっている。数学書に書かれたこのような問題を遺題という。12年後、榎並和澄(えなみともすみ)は初めて『塵劫記』の遺題の解答を自分の著書『参両録(さんりょうろく)』のなかに示した。『参両録』には新しく遺題8問が提出されたので、ここに遺題継承というリレー式の問答が始まった。『塵劫記』から始まった遺題継承は大流行し、前者の遺題の解答と自分の出題を掲載する数学書が多く出版された。また、遺題も100問、150問と多くなり、なかには前者の遺題の解答と自己の出題だけの数学書も現れた。数学の内容は急激に高度化し、17世紀末には、行列式、高次方程式、不定方程式などの高等数学が研究されるようになった。遠藤利貞(としさだ)は遺題の系譜を、『塵劫記』から始まる第一系のほかに、『数学乗除往来』『算法勿憚改(ふつだんかい)』『算法樵談集(しょうだんしゅう)』から始まる系譜をそれぞれ第二系、第三系、第四系と分類している。しかし、実際に後世に大きな影響を与えたのは第一系だけで、とくに『塵劫記』の遺題第一〇問の「円截積(えんさいせき)」は、18世紀初頭の無限級数展開を生むきっかけを与えている。関孝和(せきたかかず)や建部賢弘(たけべかたひろ)らは、第一系により数学者として大成したといってよい。

［下平和夫］

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