Dalle trasformazioni quadratiche alle trasformazioni birazionali. Un percorso attraverso la corrispondenza di Luigi Cremona

It is quite well-known the dependence of Cremona’s idea from the works of Magnus, much less known, however, and cited mostly second-hand, it seems to be the connection between the birth of birational transformations and Schiaparelli’s article of 1862. Just as are little known considerations on the history of the quadratic transformations appeared in the correspondence Cremona-Hirst. Therefore the aim of this work is to trace the origins of birational transformations making use also of the correspondence with Hirst and Schiaparelli.