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

Uma leitura dos exercícios dos excursos n Os Lusíadas

The Lusiads is an epic poem, written by Luís de Camões, about the adventure of Vasco da Gama s trip and the history of Portugal. It's based on traditionals epics from the Greek and Roman poets, Homero and Virgílio. Camões followes especially their structures. However, the poet insert modifications that divert his poem from parameters established by Aristóteles for the classic epic poems. These deviations are centered mainly on the narrative subject and in the point of view. We intend to show an analysis focused on digressions from The Lusiads, in which the author, himself or by tellers characters, narrates the story in order to make his complaints, reflections and exhortations. Besides, we present general aspects of Maneirismo predominant in these digressions how evidences of modernity of the poem; as one brief outlook about the poem's projection in time and around the world. These points are importants elements of consolidation of a universal permanence of The Lusiads. That's why they have had to read and to study by the centuries, according the vision of the epoch's spirit

As estruturas sociais e econômicas do Império Romano do Ocidente e o estabelecimento do reino dos visigodos nas Galliae Aquitania e Narbonensis

In the year 376 of the Common Era, a tribe of Germanic warriors known as Tervingi , of Gothic extraction, crossed the Hister (Danube) river due south, entering the Roman Empire. They fled the Huns, a nomadic group that came plundering their way from the East. It did not take long for a conflict between the Roman imperial authorities and the refugees to begin. Peace was reached in 382 and, henceforth, the Tervingi would be officially foederati (allies) of the Romans, gaining the right to remain an autonomous tribe inside the borders of the Empire. For the next thirteen years the Tervingi warriors fought beside the Roman imperial armies in every major conflict. Nevertheless, after the death of the emperor Theodosius I in 395, their relations deteriorated severely. In theory, the Tervingi remained Roman allies; in practice, they begun to extort monies and other assets from the emperors Honorius and Arcadius. The sack of Rome by the Tervingi king Alaric in 410 was both the culmination and the point of inflection of this state of affairs. During the 410s the Tervingi warriors would fought again beside the Roman Imperial armies and be rewarded with a piece of land in the southwestern portion of the Gallic diocese. Dubbed Visigoths , they would remain trusted Roman allies throughout the next decades, consolidating their own kingdom in the process. This dissertation deals not only with the institution of the Visigothic kingdom in the southwestern portion of the Galliae but also with the social and economic conditions that hindered the Roman ability to defend their territory by themselves, hence opening opportunities for foederati like the Tervingi to carve out a piece of it for themselves.