The quartic equation: invariants and Euler’s solution revealed

2009/03/01 by R. W. D. Nickalls · 3 citations
Mathematics · #History and Theory of Mathematics #Mathematics and Applications

paper · doi:10.1017/s0025557200184190

openalex publication_date 2009/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/05

Abstract

The central role of the resolvent cubic in the solution of the quartic was first appreciated by Leonard Euler (1707-1783). Euler's quartic solution first appeared as a brief section (§ 5) in a paper on roots of equations [1, 2], and was later expanded into a chapter entitled ‘Of a new method of resolving equations of the fourth degree’ (§§ 773-783) in his Elements of algebra [3,4].

Citations

• A new approach to solving the cubic: Cardan’s solution revealed
• A conjecture on the forms of the roots of equations

Cited by

• Setting up tunneling conditions by means of Bohmian mechanics
• Solitons in a chain of charge-parity-symmetric dimers
• Leonhard Euler [wikipedia]

Related

• A conjecture on the forms of the roots of equations
• A Note on Quartic Equations with only Trivial Solutions
• A new approach to solving the cubic: Cardan’s solution revealed
• Explicit expressions for real roots of a quartic equation
• Felix Klein's "About the Solution of the General Equations of Fifth and Sixth Degree (Excerpt from a letter to Mr. K. Hensel)"