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Dutch Algebra and Arithmetic in Japan before the Meiji Restoration


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This paper gives an overview of the scarce occasions in which Japan came into contact with Western arithmetic and algebra before the Meiji restoration of 1868. After the refutation of persistent claims on the influence through Japanese students at Leiden during the seventeenth century, it concentrates on the reception of Dutch works during the last decades of the Tokugawa shogunate and the motivations to study and translate these books. While some studies based on Japanese sources have already been published on this period (Sakaki [1994a, 2002]) , this paper draws from Dutch sources and in particular on witness accounts from Dutch officers at the Nagasaki naval school, responsible for the instruction of mathematics to selected samurai and rangakusha. Two Japanese textbooks on arithmetic from that period are viewed within the context of this naval training school.
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... The Chinese rings feature as a well-known puzzle in many works on recreational mathematics. It is covered in all the classic works such as [22,, [3,[80][81][82][83][84][85], [8,Problem 417] and [12,[15][16][17]. In French nineteenth-century works ( [22], [13]), the puzzle is also known by the name 'Baguenaudier'. ...
... Furthermore, there is the case of Hartsingus, a 'Japanese student' of mathematics at Leyden in 1654. However, none of these supposed influences can pass closer scrutiny [16]. A further complication is that the Japanese version of the problem, known as mamakodate, also features in literary works of a much older date. ...
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The Chinese rings puzzle is one of those recreational mathematical problems known for several centuries in the West as well as in Asia. Its origin is diffcult to ascertain but is most likely not Chinese. In this paper we provide an English translation, based on a mathematical analysis of the puzzle, of two sixteenth-century witness accounts. The first is by Luca Pacioli and was previously unpublished. The second is by Girolamo Cardano for which we provide an interpretation considerably different from existing translations. Finally, both treatments of the puzzle are compared, pointing out the presence of an implicit idea of non-numerical recursive algorithms.