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Register a new userFelix Kleins About the Solution of the General Equations of Fifth and Sixth Degree (Excerpt from a letter to Mr. K. Hensel)
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Alexander J. Sutherland
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This is an English translation of Felix Kleins classical paper Uber die Auflosung der allgemeinen Gleichungen funften und sechsten Grades (Auszug aus einem Schreiben an Herrn K. Hensel) from 1905 and is put in modern notation. The original work first appeared in the Journal for Pure and Applied Mathematics (Volume 129) and then was reprinted in Mathematische Annalen (Volume 61, Issue 1). Kleins work (including his Lectures on the Icosahedron and the Solution of Equations of Fifth Degree) lies at the heart of the 19th and 20th work on solving generic polynomials. In this paper, Klein summarizes his approach to solving the generic quintic and sextic polynomials. He also lays the foundation for the modern framework of resolvent degree.
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This is a translation of Kroneckers Uber die Gleichungen funften Grades (On equations of fifth degree), excerpted from the monthly report to the Berlin Academy of Sciences from June 1861.
We translate Erland Samuel Brings treatise Meletemata quaedam Mathematica circa Transformationem Aequationum Alebraicarum (Some selected mathematics on the Transformation of Algebraic Equations) written as his Promotionschrift at the University of Lund in 1786, from its Latin into English, with modern mathematical notation. Bring (1736 - 98) made important contributions to algebraic equations and obtained the canonical form x^5+px+q = 0 for quintics before Jerrard, Ruffini and Abel. In due course, he realized the significance of the projective curve which now bears his name: the complete intersection of the homogeneous Fermat polynomials of degrees 1,2,3 in CP^4.
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