Calculus Without Limits

The Greek of the classical age, with Euclid and Archimedes, have conceived very next ideas to those that have allowed the invention of the Infinitesimal and Integral calculation. The author thinks how just Euclide has grazed the concept of infinitesimal, with his theorem related to the "horn angle." It was then in 1600 that Leibniz and Newton they created the Infinitesimal Calculus and that Integral. But the infinitesimals have always elicited criticisms for their logical contradictions, immediately stigmatized by the bishop Berkeley. With the method of the double limit of Weierstrass, the problem apparently, seems overcome. Then in the 1900 Robinson overcome the impasse from the logical point of view, but resorting to the Analysis not-standard, in the sphere of not Archimedean fields. With this work the author overcomes the issue of the infinitesimals, adopting a very classical methodology and, above all, of easy understanding.