Erland Samuel Bring's "Transformation of Algebraic Equations"

TL;DR

This paper translates Erland Samuel Bring's 1786 treatise on algebraic equation transformations into modern English and notation, highlighting his pioneering work on quintic equations and projective curves.

Contribution

It provides the first English translation and modern interpretation of Bring's influential work, emphasizing his early contributions to algebra and algebraic geometry.

Findings

Bring's canonical form for quintic equations x^5+px+q was established before Jerrard, Ruffini, and Abel.

He recognized the importance of the projective curve now named after him.

The translation makes Bring's historical mathematical insights accessible to modern scholars.

Abstract

We translate Erland Samuel Bring's 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.