He was very influential in bringing about reforms in the secondary schools of Italy and became a leader in questions of mathematical pedagogy as well as in those relating to the advancement of knowledge.

The mathematical advances which Italy made since the middle of the nineteenth century were largely guided by Cremona, Brioschi, and Beltrami.

In this same year he competed for the Steiner Prize of the Berlin Academy, with a treatise entitled Memoria sulle superfici del terzo ordine, and shared the award with J. C. F. Sturm.

Papers by him appeared in the mathematical journals of Italy, France, Germany and England, and he published several important works, many of which have been translated into other languages.

His manual Graphical Statics and his Elements of Projective Geometry (translated by Thomas Hudson Beare and C. Leudesdorf respectively) were published in English by the Clarendon Press.