Sentence:  The arithmetic theory of binary <WSD>quadratic forms</WSD>, which had its origins in the work of Fermat, was extensively developed during the 18th century by Euler, Lagrange, Legendre and Gauss. The extension to <WSD>quadratic forms</WSD> in more than two variables, which was begun by them and is exemplified by Lagrange's theorem that every positive integer is a sum of four squares, was continued in the 19th century by Dirichlet, Hermite, H. J. S. Smith, Minkowski and others. 
Meaning of the word marked with <WSD> tags:  A homogeneous polynomial of degree 2 in a given number of variables.