Luigi Cremona and Wilhelm Fiedler: the link between descriptive and projective geometry in technical instruction

This paper considers Luigi Cremona’s and Wilhelm Fiedler’s outlook on technical instruction at school and university level, their vision about the educational role of descriptive geometry and its relation to Monge’s original conception. Like Cremona, Fiedler sees a symbiosis between descriptive and projective geometry via the fundamental idea of central projection. The link between projective and descriptive geometry plays a double role: an educational one due to the graphical aspects of the two disciplines and a conceptual one due to the connection of theory to practice. Thus, projective and descriptive geometry contribute to form a class of scientifically educated people, and the link between them epitomizes – in the opinion of Cremona – the link between pure mathematics and its applications. According to Fiedler, the main scope of the teaching of descriptive geometry is the scientific construction and development of “Raumanschauung”, as stated in a paper published in the Italian journal Giornale di Matematiche. The textbooks by Fiedler (1871) and Cremona (1873) were used in Italy to develop the geometry programs for the sezione fisico matematica (physics and mathematics section) within technical secondary instruction. While the relation between projective and descriptive geometry – and, thus, between pure and applied mathematics – had a short life at secondary school level in Italy, at the turn of the century there was a new expansion at university level due to the important role that then mathematicians had in the creation of the Faculty of Architecture.