Summary:
Two of the basic mathematical problems that led to the invention of Calculus were the problem of determining the area under a curve and the problem of the tangent. The present dissertation is a bibliographic review of the tangent problem that occupied the great mathematicians of the 17th century. The series of chapters is based on the chronological map of the various methods of tangent construction, starting from the roots of the problem in antiquity, until the end of the 17th century when the inverse tangent problem is added and finally the invention of Calculus. Fermat and Descartes were the first to apply the tools of algebra to the geometry of curves, developing separately, systematic methods for finding the tangent, but which were effective only in curves of the form y = f (x), where f is a polynomial. At the same time Roberval approaches the problem based on the kinematic method, while a little later Hudde develops more efficient methods in curves of the form y = f (x), where f is a polynomial, and Sluse develops rules for curves of the form y = f (x, y), where f (x, y) is a polynomial of two variables. The introduction of these rules was soon followed by identical methods of infinitesimal character, with Barrow as an important representative, who, together with Gregory at about the same time, were the first to publish a proof of the Fundamental Theorem of Calculus, although none of them realised its importance. The baton is taken by Newton and Leibniz, who give us the ability to calculate a large number of areas, manage differential equations, etc., and for this reason are considered the inventors of Infinitesimal Calculus. By the end of the 17th century the tangent problem was fully integrated into the general rules of derivatives, Newton's "Fluxional" methods and Leibniz's "Differential" methods.
Keywords:
tangent, area, inverse tangent problem, Fundumental Theorem, Calculus
