 Abbati's investigations and exchanges with Ruffini also examined diophantine equations, prime numbers, the specification of the number of imaginary roots as compared with the results of P. Paoli, the relation among the roots and the coefficients of an equation, the Cartesian rule for incomplete equations, the properties of permutations of the roots of quartic and quintic equations, the equation of differences, rational functions of roots, resolution by approximation and the related Lagrange multipliers.The thirty letters which Abbati wrote to Ruffini are now housed in the Ruffini Archive of the Biblioteca Estense in Modena.All the letters remain unpublished except one published by E. Bortolotti in an edition of Ruffini's correspondence.