 In his book "Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas", Harriot drew, in a first section, tables for addition, subtraction, multiplication and division of monomials, binomials, and trinomials.Then, in a second section, he set up the equation , and showed that this matches the form of multiplication he had previously provided, giving the factorization .The following methods apply to any expression that is a sum, or that may be transformed into a sum.