Uma ideia sobre o conceito de limite ao longo da história da matemática

Abstract

This work seeks to understand how it developed the concept of limit along part of the history of mathematics, from its most rudimentary forms, going through some contributions of Greek Mathematics, also bringing some contributions of mathematics developed in Medieval Europe and then some contributions of Bonaventura Cavalieri (1598-1647). We also seek to understand the di culties faced by mathematicians of this period to understand the concepts related to limit, such as: in nitely small , in nitely large , indivisibles, sum of in nite sequences, etc. In relation to some concepts of limit present in the Greek Mathematics, we highlight some paradoxes of Zeno of Elea ( 460 b.C.e.), the idea of the indivisibles and some contributions of the book The Elements . Later, still related to the Greek Mathematics, we focus on some works of the Archimedes of Syracuse ( 287-212 b.C.e.) about the quadrature of the circle, the quadrature of the parabola and about the spirals. Then, we bring some concepts of limit present in the Medieval Europe, highlighting some discussions about in nity. We end this work with some contributions of Cavalieri to the Integral Calculus. We can see, even if implicitly, a primitive concept of limit in several of the presented moments, such as: in approximations to area of the circle, in the use of in nite sums, in the discussion about the indivisibles, in the use of the limit of the areas of gures circumscribed and/or enrolled for the calculating of the area of curves gures.