The aim of this work is to present an educational path developed in the classroom built up by using examples, taken from the history of mathematics, to show some elements of connection between geometry and algebra. This path was carried out with third-year students at an upper secondary school in Italy. The choice of the historical material used was supported by the idea of constructing a simple environment to effectively explore the potential of some forms and registers through which mathematics expresses itself, to ascertain how changes between these registers can take place and to evaluate the typologies of responses that such changes can produce when solving a problem. Some questions, proposed to the students with the aim to collect their opinions on the link between geometry and algebra, were followed by the reading of selected passages taken from original sources in the history of mathematics, in which the latter assumed the role of a tool for conveying conscious knowledge. In these passages the relevant mathematical elements, the different expressive registers used and their role in the search for the solution of the problem, have been identified. Finally, we collected some impressions and effects that the experience has aroused in the students, drawing some conclusions.