He also studied quadratic forms in full generality (as opposed to m X 2 + n Y 2 {\displaystyle mX^{2}+nY^{2}} )—defining their equivalence relation, showing how to put them in reduced form, etc. Adrien-Marie Legendre (1752–1833) was the first to state the law of quadratic reciprocity.
Tamén estudou as formas cadráticas dun xeito xeral (en oposición a m X 2 + n Y 2 {\displaystyle \scriptstyle mX^{2}+nY^{2}} ), definindo a súa relación de equivalencia, amosando como poñelas na forma reducida etc. Adrien-Marie Legendre (1752–1833) foi o primeiro en establecer a lei da reciprocidade cadrática.