Vector calculus in the didactics of mechanics in Italy in the early twentieth century

Dell'Aglio, Luca ; Freguglia, Paolo

Matematica, cultura e società, Série 1, Tome 8 (2023) no. 3, pp. 251-270

Résumé

Firstly, we have provided a historical outline of the geometrical calculus and geometrical algebra during the second part of XIX century and the first years of XX century. Subsequently, our aim has been to highlight through this period in Italy, and in the international context (comparison with Eugène Prouhet (1817-1867), Charles Sturm (1803-1855), Gustav Robert Kirchhoff (1824-1887), Osip Ivanovich Somoff (1815-1876), Paul Appell(1855-1930), Otto Föppl (1854-1924) and others) the didactic use of geometrical calculus (and of the homographies) in the university treatises of mechanics and of mathematical physics. In this historical overview, we have analyzed the textbooks of Ottaviano Fabrizio Mossotti (1791-1863), Gian Antonio Maggi (1856-1937), Pietro Burgatti (18681938) and those of the Peanian tradition (Filiberto Castellano, Cesare Burali-Forti, Roberto Marcolongo, Tommaso Boggio). Section Four is devoted to the description of homography synthetic theory in teaching classical mechanics in the Italian vector school: homography as an extension of the minimum system. Our considerations about the Tullio Levi-Civita and Ugo Amaldi textbook are presented in Section Five. The essential role of the minimum system is evident in our previous analyses. From this, one can develop other concepts (such as the homographies) and introduce new operators. Giovanni Giorgi (1871-1950), a physicist and mathematician emblematic as critic on the techniques proposed by the vectorialists, states Burali-Forti and Marcolongo's methods are “too compact and difficult to read”. However, according to Giorgi, one of the merits of their work was the depth of the theory of vector homographies.