Cubic equations in the casus irreducibilis (Study of the History of Mathematics 2022)

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Bibliographic Information

Other Title
  • 3次方程式の還元不能な場合

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Description

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.

Journal

  • RIMS Kokyuroku Bessatsu

    RIMS Kokyuroku Bessatsu B92 1-24, 2023-07

    Research Institute for Mathematical Sciences, Kyoto University

Keywords

Details 詳細情報について

  • CRID
    1050297272079682816
  • NII Book ID
    AA12196120
  • HANDLE
    2433/284812
  • ISSN
    18816193
  • Text Lang
    ja
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB

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