From quadratic to birational transformations. A survey of the correspondence of Luigi Cremona (Q2831537)

This paper reconstructs the birth of Cremona's transformations of plane figures. In particular, the debt that Luigi Cremona had with respect to the previous work of Giovanni Virginio Schiaparelli, and the fruitful intellectual and epistolary exchange with Thomas Archer Hirst are investigated. The reciprocal influence of the latter mathematician on Cremona is analyzed in more detail. Several examples of quadratic transformations from the work of these two mathematicians are briefly recalled and illustrated by figures. NEWLINENEWLINENEWLINE NEWLINEThe main motivation of the paper can be found in the author's own words claiming that ``the historical problematic concerning quadratic transformations (\dots) seems to have been disregarded by historians of mathematics''. Hence, this paper may serve to provide the readers with the necessary information appropriate to recover some of the fundamental steps that brought to their discovery.