Problemas e modelos que contribuíram com o desenvolvimento do cálculo diferencial e integral: dos gregos à Newton

This article refers to a research which tries to historically (re)construct the conceptual development of the Integral and Differential calculus, taking into account its constructing model feature, since the Greeks to Newton. These models were created by the problems that have been proposed by the history and were being modified by the time the new problems were put and the mathematics known advanced. In this perspective, I also show how a number of nature philosophers and mathematicians got involved by this process. Starting with the speculations over scientific and philosophical natures done by the ancient Greeks, it culminates with Newton s work in the 17th century. Moreover, I present and analyze the problems proposed (open questions), models generated (questions answered) as well as the religious, political, economic and social conditions involved. This work is divided into 6 chapters plus the final considerations. Chapter 1 shows how the research came about, given my motivation and experience. I outline the ways I have gone trough to refine the main question and present the subject of and the objectives of the research, ending the chapter showing the theoretical bases by which the research was carried out, naming such bases as Investigation Theoretical Fields (ITF). Chapter 2 presents each one of the theoretical bases, which was introduced in the chapter 1 s end. In this discuss, I try to connect the ITF to the research. The Chapter 3 discusses the methodological choices done considering the theoretical fields considered. So, the Chapters 4, 5 and 6 present the main corpus of the research, i.e., they reconstruct the calculus history under a perspective of model building (questions answered) from the problems given (open questions), analyzing since the ancient Greeks contribution (Chapter 4), pos- Greek, especially, the Romans contribution, Hindus, Arabian, and the contribution on the Medium Age (Chapter 5). I relate the European reborn and the contribution of the philosophers and scientists until culminate with the Newton s work (Chapter 6). In the final considerations, it finally gives an account on my impressions about the development of the research as well as the results reached here. By the end, I plan out a propose of curse of Differential and Integral Calculus, having by basis the last three chapters of the article

A dinâmica do pensamento geométrico :aprendendo a enxergar meias verdades e a construir novos significados

This work is a case study to investigate the dynamics of the historians thought as they produce a knowledge about the history of the area measurement systems as forms of historical expressions and representations. We refer to some of the ideas of David Bohm (1989, 1992, 1994, 1996) to support our theoretical understanding about the operation of thought. We chose a period that is recognized by the theorists as the origin of the geometrical thought -embracing the knowledge developed by the Egyptians, Babylonians, Chinese, Hindus, Greeks and Romans- and is referred to as containing a cycle in the development of this knowledge, described as beginning, apogee and decline. We assume this history, as told by the theorists, as a version that we organize and tell with the help of three sets of categories. The first refers to the elements that take part in the measurement practices; the second refers to the historians understanding about the development of the scientific knowledge. This exercise allowed us to extract the theorists main beliefs, that we criticized in the light of the knowledge about Cubação (Dal Pian, 1990). We stress the importance of the methodological approach adopted in this study to the teaching of Geometry and its history