- In 1826 Cauchy, in the context of quadratic forms in n variables, used the term ‘tableau’ for the matrix of coefficients.
- Find the 2 roots and a continued fraction for a root of these quadratic equations.
- He was able to use his methods to prove many results in the theory of quadratic forms and number theory.
- If f = 0, then the quartic in y is actually a quadratic equation in the variable y 2.
- Smith also extended Gauss's theorem on real quadratic forms to complex quadratic forms.