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Among his works are “Sopra alcune formule e serie infiniterelative ai fattoriali ed agli integrali euleriani,” in Annali delle scienze del Regno Lombardo Veneto, 4 (1834,), 10-19; “Teoremi generali per determinare le aree dei poligoni ed i volumi dei poliedri col mezzo delle distanze dei loro vertici,” in Annali Fusinieri (1834); “Saggio di applicazioni di un nuovo metodo di geometria analiticacalcolo delle equipollenze,” ibid., 5 (1835); “Memoria sul metodo delle equipollenze,” in Annali delle scienze del Regno Lombardo Veneto, 7 (1837), 243–261; 8 (1838), 17–37, 85–121; “Sul movimento di un liquido che discende in modo perfettamente simmetrico rispetto a un asse verticale,” in Atti dell’Istituto veneto, 3 (1844), 206–210, and Memorie dell’Istituto veneto, 2 (1845), 339–360; “Sul più facile modo di trovare le radici reali delle equazioni algebriche a sopra un nuovo metodo per la determinazione delle radici immaginarie,” ibid., 3 (1847), 109-220; “Considerazioni sulle nomenclature chimiche, sugli equivalenti chimici e su alcune propiretà, che con questi si collegano,” ibid., 221-267; Lezioni di geometria descrittiva (Padua, 1851, 1858): “Sulla classificazioni delle curve del terzo ordine,” in Memorie della Società italiana delle scienze (dei Quaranta), ser. Loria, Storia delle matematiche, III (Turin, 1933), 500–501; E. Peano, Calcolo geometrico secondo l’Ausdehnungslehre di.

He also began the classification of curves of class three.

226.]Thus we are given a kind of algebra analogous to that of complex numbers with two units; it found its application in various problems of plane geometry and mechanics, and paved the way for W. Hamilton’s ton’s theory of quaternions (1853), through which geometric calculus can be applied to space; it also led to Grassmann’s “Ausdehnungslehre” (1844), and finally to the vector theory.

With his barycentric calculus, Bellavitis created a calculus more general than Moebius’ “baricentrische Calcul.”In 1834, in his formula expressing the area of polygons and the volume of polyhedra as a function of the distances between their vertexes, Bellavitis anticipated results that were later newly discovered by Staudt and published in 1842.

On 15 March 1850, Bellavitis became a fellow of the Società Italiana dei Quaranta, and in 1879 a member of the Accademia dei Lincei In 1866 he was named a senator of the Kingdom of Italy.

Bellavitis’ method of equipollencies belongs to a special point of view in mathematical thought: geometric calculus.

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During this period he published his first major works, including papers (1835, 1837) on the method of equipollencies, which were hailed as one of his major contributions.

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