A teoria dos indivisíveis: uma contribuição do padre Bonaventura Cavalieri

Abstract

This dissertation intends to highlight a contribution to mathematics by Bonaventura Cavalieri (1598-1647) through his studies about the indivisibles, better known as Treaty of Cavalieri, concerning the calculation of areas and volumes. Cavalieri s work, Geometry of indivisible , was analysed including the practical application of his theory and some of the criticism and its possible causes. Taking these studies into consideration, a summary about the ancient Greeks ideas, such as the concepts of atomism and the theory of minima naturalia, was developed. It includes the ideas of Zeno (495 - 430 BC) and Aristotle (384-322 BC) and the Archimedes (287-212 BC). The translators of Aristotle in the Middle Age were also studied, and so were the ideas, applications and conclusions about the infinitely small and indivisible, developed by Johannes Kepler (1571-1630) and Galileo Galilei (1564-1642) during the seventeenth century. Bonaventura Cavalieri shows an unusual bias for the seventeenth century, but which allows the use of a generic method. He researched a rational systematization of the method and the position across from the indivisible. It made it possible to study them in an indirect way, without positioning himself about the composition of continuous, and considering an indirect link between the continuous and the atoms of magnitude