A general method for investigating the roots of all equations by approximation

TL;DR

This paper discusses a general approximation method for finding roots of all equations, building on Euler's series for polynomial roots, aiming to provide a universal approach to root investigation.

Contribution

Introduces a comprehensive approximation technique for solving all types of equations, extending Euler's series approach for polynomial roots to a broader class of equations.

Findings

Developed a series-based method for root approximation

Applicable to all equations, not just polynomials

Builds on Euler's earlier work for polynomial roots

Abstract

Translation of the Latin original, "Methodus generalis investigandi radices omnium aequationum per approximationem" (1776). E643 in the Enestrom index. Euler gives a series to find powers of roots of polynomials.