  In Disquisitiones Arithmeticae, Gauss studied binary quadratic forms and
introduced a very general version of a composition operator that allows
composing even forms of different discriminants and imprimitive forms. Section
V of Disquisitiones contains truly revolutionary ideas and involves very
complicated computations, sometimes left to the reader. With this theory, Gauss
develops a method of factorization using quadratic residues obtained by binary
quadratic forms. In this work we explore Gauss method making many of the
computations necessary to better understand his work.
