Applicazioni geometriche del calcolo infinitesimale

The book Applicazioni geometriche del calcolo infinitesimale (Geometrical Applications of Infinitesimal Calculus), published in 1887 by Giuseppe Peano, introduced fundamental elements of geometric calculus. Peano, an Italian mathematician and a pioneer in symbolic logic, explored new definitions for arc length and the area of curved surfaces. His work contributed to the formal development of mathematics, emphasizing rigorous logic and notation.

The concept of the infinitesimal, a quantity smaller than any finite number but not zero, was historically crucial in the development of calculus. Early calculus, often called infinitesimal calculus, used infinitesimals to define derivatives and integrals. While not part of the real number system, these concepts laid the groundwork for modern calculus and its applications in geometry.123