Formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva

The inclusion–exclusion principle is a simple, intuitive, and extremely versatile result. It one of the most useful methods for counting it can be used in different areas mathematics. In eighteenth century, first uses this result that appear literature are related to study problems games chance. However, formulations appear, independently by several authors, only nineteenth century. article, we obtained Adrien-Marie Legendre, Daniel Augusto da Silva, James Joseph Sylvester, Henri Poincaré. We highlight contribution Portuguese mathematician since his formulation applied number theory, whenever collections numbers satisfying certain properties involved, reason why stands out compared with all others.