In this paper, we study types and roles of visualization in four historic key moments: Greek geometry with Euclid's Elements and Hérigone; Algebra in Renaissance with Jerome Cardan and Jacques Peletier du Mans; Cartesian geometry in 17th century with René Descartes and Bernard Lamy; Logic with Gottfried Leibniz and John Venn. For this purpose, we use the classification of signs and the design of diagrams of Charles Sanders Peirce. It leads us to a semiotic history which is rich in reflections on teaching practices with the aim, in particular, of enabling teachers to explain to students the role and meaning of signs, but also that of diagrams in mathematical practice.