The teaching of mathematics in the Casati law: the case of descriptive geometry

Nowadays descriptive geometry is no longer part of the mathematics syllabuses in Italian secondary schools. The representation methods that are the focus of this subject are currently almost only covered in technical drawing courses. They have been stripped of their theoretical structure and therefore considered nothing more than a technical graphic representation. Today, because of computers, and skilful use of software, which allows the graphic representation of any object with no knowledge of the principles of geometry that underlie the representation method used, this subject is even being eclipsed from the University curricula, where it is often relegated to the role of a minor subject in the faculties of Engineering and Architecture.
In the 19^th century, the situation was very different from the present. Descriptive geometry used to represent one of the most important branches of Applied Mathematics and, as such, was part of the fundamental subjects in the Mathematics and Engineering degree courses. In fact in 1860, with the application of implementing regulations for the first systematic law on Education in Italy – the Casati Law (1859) – descriptive geometry was instantly introduced as a subject for technical secondary schools. In this work we will analyse some of the historical aspects connected to the creation of this specific curricula.