He had a PhD in Mathematics, was Lieutenant Colonel of Infantry and a reader in Coimbra. The main contribution of Augusto Fonseca was related to the theme of his inaugural dissertation, the quaternions, a subject he published several works about. At the service of the University of Coimbra, he was a lecturer of the course of Descriptive Geometry with intervals for him do to his military work. Along with Alfredo Felgueiras da Rocha Peixoto and Francisco Miranda da Costa Lobo, he prepared a draft of the Reform Project of the Faculty of Mathematics of the University of Coimbra. He ended his academic career in a controversy with the University.
Keywords: mathematics; quaternions; reader at the University of Coimbra; army; Lieutenant Colonel of Infantry.