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

A retórica em Aristóteles: da orientação das paixões ao aprimoramento da eupraxia

This research brings into focus the relationship between the work Rhetoric, from Aristotle, and the conceptions of ethics and practical wisdom of the philosopher from Stageira. Accordingly, it attempts to show that Aristotle's Rhetoric was produced to guide the construction and orientation of oratory passions of the Greek man, setting it as a reference for practices aimed at social ordering of the polis. In other words, the Aristotelian Rhetoric, designed by the author as the study of what is persuasive in every speech, is not composed with the meaning of persuasion at any cost, in another sense it is conceived by Aristotle as a useful knowledge for the improvement eupraxic (the good act in accordance with the fair and true). This research finds that such work has been prepared by Stagirite a time of strong social transformations and upheavals in ancient Greece: The skepticism expanded, with each person wanting to live their own businesses, and especially in Athens, a city that served as intellectual and political reference, there was a lack of collective spirit. In this tumultuous social environment, Aristotle, with a culture of Greeks eager Trusted reviews and socially shareable in the field of verisimilitude, sought with his Rhetoric, contributing to the development of ethics and political science; referrals for legal and organization of inter-social relations in varied environments, including seeking to provide knowledge about human passions and emotional status of active citizens in deliberative meetings

Sonho e cura: o culto de Asclépio em Epidauro entre os séculos IV e II a. C.

Profound changes have marked Greek society from the fourth century B.C.. Conquests, wars and epidemics altered drastically the Greek’s posture regarding his public life, his conception of gods and hence the construction of their spaces, whether sacred or profane. Through the fonts, we perceived that the cult of god Asklepeios turned very popular, in this context, for the peculiar way that the god relates to his devotees, through the dreams. We know that the dream was held, for the Greeks, as a space of real existence, it was sacred, and could be accessed in the healing rituals of Asklepios. Our work intends, thereby, to understand the curious and peculiar oniric space, mainly through the inscriptions, architectural structures of the sanctuary and the ancient texts that refer to the context of the period, because we understand that this space was the essential condition for the popularization of the cult, it placed the individual in direct contact with the divinity, a rare closeness between men and gods accepted by the greek imagery until then.