On the acceptance of trigonometry in wasan: Evidence from a text of Aida Yasuaki

The Dutch introduced trigonometry to Japan in the middle of the 17th century, but the use of trigonometry was rarely seen until the 18th century, and its use was limited to practical purposes such as surveying and astronomy. It was rarely used to solve geometry problems currently called wasan, the r...

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Bibliographic Details
Published in:Historia mathematica 2020-08, Vol.52, p.51-65
Main Author: Unger, J. Marshall
Format: Article
Language:English
Subjects:
Approximation
Power series
Regular polygons
Trigonometry
Wasan
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Summary:The Dutch introduced trigonometry to Japan in the middle of the 17th century, but the use of trigonometry was rarely seen until the 18th century, and its use was limited to practical purposes such as surveying and astronomy. It was rarely used to solve geometry problems currently called wasan, the reason for which is not yet fully explained. In this paper, I summarize a book by Aida Yasuaki (1747–1817) in which he strongly criticizes the use of trigonometry for wasan, and try to find the origins of his antipathy. オランダ人が日本に三角法を紹介したのは17世紀中ごろであったが、 それは18世紀までめったに使われず、使われてもだい たい測量や天文学など実用的な目的に限られ、和算と現在呼ばれる幾何の問題を解くのに使用されることはほとんどなかった。 その理由については、今まで十分に 説 明されて来なかった。この論文では、会田安明 （1747-1817） が一つの和算問題を取り 上げて、 その解決に三角法を使用した人を強 く批判した本の内容を詳しく 説明し、彼の反感の起源を見つけようと試みている。
ISSN:0315-0860
1090-249X
DOI:10.1016/j.hm.2020.06.004