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| ファイル | 記述 | サイズ | フォーマット | |
|---|---|---|---|---|
| B92-01.pdf | 486.19 kB | Adobe PDF | 見る/開く |
| タイトル: | 3次方程式の還元不能な場合 |
| その他のタイトル: | Cubic equations in the casus irreducibilis (Study of the History of Mathematics 2022) |
| 著者: | 長田, 直樹  |
| 著者名の別形: | Osada, Naoki |
| キーワード: | 01A40 01A45 cube root of binomial cubic equation casus irreducibilis angle trisection |
| 発行日: | Jul-2023 |
| 出版者: | Research Institute for Mathematical Sciences, Kyoto University |
| 誌名: | 数理解析研究所講究録別冊 |
| 巻: | B92 |
| 開始ページ: | 1 |
| 終了ページ: | 24 |
| 抄録: | When a real cubic equation has three distinct real roots, it is called the casus irreducibilis or the case of irreducible. To find the roots of such equations using Cardano's formula, it is necessary to extract cube roots of imaginary binomials. In this paper we review remarkable works from Cardano to Euler on the solution of cubic equations in the casus irreducibilis and on the extraction of the cube roots of imaginary binomials. In it we give new proofs of Girard's method of constructing three real roots of a cubic equation and of Newton's method of extracting cube roots of imaginary binomials. |
| 著作権等: | © 2023 by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. All rights reserved. Printed in Japan. |
| URI: | http://hdl.handle.net/2433/284812 |
| 出現コレクション: | B92 Study of the History of Mathematics 2022 |
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