日本における「てこの原理」の数学的理解の歴史

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In this paper, we researched into the subject of when and how the Japanese came to comprehend "the principle of leverage" - the concept of moment - mathematically. Our method of treating the subject was to seek out the literature on mathematics published in the Edo period which contain those problems that require the mathematically strict comprehension of the principle of leverage, on the assumption that the "steelyard" being an ordinary tool for weighing in the Edo period, there might be some books which give the reason why it is possible to weigh accurately with a steelyard. The results, however, showed that none of those books published in Japan by the 18th century - i. e. before the introduction of "Rangaku" (Dutch learning in Japan) - treated such problems systematically. Therefore we decided to search for books which contained problems requiring, even if only fragmentarily, the mathematically strict comprehension of the principle, and finally found seven books of this type. The problems which are treated in these books can be divided into two categories: (1) One is "the problems relating to the steelyard," treated in Cheng's Sampo-ttiso (rendered from Chinese into Japanese by Yuasa, 1676) and Nakane's Kanja-otogis'oshi (1743). The former, however, gives an incorrect answer, owing to the fact that it neglects the difference between the zero point of the graduations and the connecting point of the suspension cord of the steelyard. The latter points out this error and corrects it, which is indicative of the clear understanding of the concept of moment. (2) The other is "the problems of cutting out portions with as given weight from an irregular object," which is dealt with in such books as Fujioka's Sangenki (1657), an unknown author's Sangaku-chienoumi (1718), Irie's Hyakko-hijutsu (1724), Murai's Sampo-doshimon (1784) and Funayarna's Elzon-kuffi-no-nishiki (1798). None of them, however, comprehend the concept of moment, and therefore the answers are all incorrect. Then, how was the problem relating to "the principle of leverage" - the concept of moment - dealt with thereafter in the 19th century in Japan? Funayama's Ehon-kuffi-no-nishiki (1798) was criticized by Aida in his "Ehon-kufa-no-nishiki-hyorin" (dated November, 1800 in the preface). Then Aida became involved in arguments with Fujita (who wrote "Ehon-kufil-nishiki-hyo," dated March, 1801 in the preface) and Sakabe (who wrote "Ehon-kufil-no-nishiki hyoban," dated September, 1801 in the preface). And then in 1804, "Kojodaihisho" (or "Enrishoheijutsu-kaigi (Kongenjutsu)"). was anonymously released. This is the first book published in Japan that comprehends "the principle of leverage" - the concept of moment - strictly in terms of mathematics. And after the publication of Sampo-tenzan-shogakusho in 1833, "the solution to the problem of the center of gravity" became fashionably popular among the scholars of Japanese native mathematics. "Kojodaihisho" (1804), according to its preface, was written under the influence of one of the imported Chinese books of science, Verbiest's Shinsei-reidai-gishoshi (published in 1674, and introduced to Japan at the latest in 1748) - i. e. not under the influence of "Rangaku".
日本科学史学会の論文
1985-10-25

日本における「てこの原理」の数学的理解の歴史

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