A distinção cartesiana entre curvas geométricas e curvas mecânicas

Abstract

Mathematics, according to most people, is an exact science - but what it means to be exact? Or, if it is accurate, as are their objects? Exactly? Or rather, what is a mathematical object? How to differentiate a mathematical object to another? What characteristics / properties are necessary for an object to be mathematical? Be accurate means to be intelligible? These questions, which are not the subject of discussions in this work were the triggering of this study. The proposal is to discuss the Cartesian refusal of the Greek criterion of demarcation between the two types of curves and try to understand the establishment of new criteria adopted by Descartes. Thus, looking along the dissertation seek to understand the reasons that led the philosopher to discuss and reclassify the curves. To understand the Cartesian distinction between geometric curves and mechanical curves we must first present the context in which these curves appear. In this aspect, it is initially held a historical retrospect of the main curves studied and investigated by the Greeks, as well as its main geometers representatives. In this context, it is reviewed and discussed the key role of the classic problems, which influenced the appearance and desevolvimento of such curves. Are they triggered new investigations and the appearance of new curves. Following a discussion of the Geometry test is carried out, containing an overview of the work, a characterization and demarcation of curves in this area. Next is discussed the understanding of Descartes to distinguish between geometrical and mechanical curves. Finally, conclusions are drawn about the view expressed here. According to Bos (2001), the argument adopted by Descartes to classify the curves was the "philosophical analysis of gemétrica intuition", namely the construction and representation of curves served to create objects known. Behind any choice of procedures for the construction was the intuition of "known-unknown", or, in general, the certainty of intuition in geometry. The overview that fincava her stakes was that the geometry has been shaped by a philosophical concern based on the certainty of geometrical operations, particularly buildings, ie the Cartesian mathematics was (and still is) the mathematics of a philosopher, in this context, that mathematics can not posit no arguments. In this respect, it is understood that Descartes had an idea of rationality based on continuity. Continuing this presupposes that a continuous movement of insights that can be reduced in a whole or in several movements, since continuous and intelligible. For example, in a spider's web, there is a main wire which is touched, it moves all other wires. So is the intuitive continuous movement presupposed by Descartes to the understanding of a geometric curve. The continuity of the generation of a geometric object corresponds to the continuity of mathematical thinking and therefore of understanding of the object continuously.