Part of a manuscript written by the French mathematician Evariste Galois (1811-1832). Galois worked on the problem of finding general solutions for equations of degree n (ie containing terms of the form x raised to the power n, where n is an integer). Galois showed that each equation has an associated group (the Galois term) of substitutions, and that this group determines the solvability of the equation. This work formed the foundations of the branch of mathematics known as group theory.