In the 18th century there was much elaboration of previous suggestions

Toward its close La Grange and Euler made substantial advance. With the opening of the present century came Gau , Cauchy, Jacobi, Abel, Fourier, Horner, Sturm and others. Their work Salmon, Sylvester, Cayley and others have carried forward. The more recent development is in the branch called "Determinants." Hamilton and Gro man have introduced new elements in the discu ion. Pure algebra in its higher development becomes "The Theory of Equations." Algebraic notation and proce es, applied in different directions and under various conditions, sweep over the entire mathematical field.