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Previous issue date: 2010-06-25 === 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 === Esta tese de Doutorado teve como objetivo fazer uma (re)constru??o hist?rica do
desenvolvimento Conceitual do C?lculo Diferencial e Integral olhando-o como uma
constru??o de modelos, dos gregos a Newton. Tais modelos eram gerados a partir
de problemas que foram sendo propostos ao longo da hist?ria e iam sendo
modificados ? medida que novos problemas eram postos e o conhecimento
matem?tico avan?ava. Nessa perspectiva, busco tamb?m mostrar que esse
processo envolveu uma legi?o de matem?ticos/fil?sofos da natureza, tendo in?cio
com as especula??es de natureza cient?fica e filos?fica dos antigos gregos e
culmina com o trabalho de Newton, no s?culo XVII. Al?m disso, nesse processo
de reconstru??o do desenvolvimento conceitual do c?lculo apresento e analiso os
problemas propostos (quest?es em aberto), modelos gerados (quest?es
respondidas) bem como as condi??es sociais, econ?micas, pol?ticas e religiosas
envolvidas no processo. O trabalho est? dividido em seis cap?tulos mais as
considera??es finais. No cap?tulo 1 apresento como a pesquisa se configurou a
partir das minhas motiva??es e experi?ncias. Delineio os caminhos percorridos
para o refinamento da pergunta diretriz e apresento o objeto de e os objetivos da
pesquisa e fecho o cap?tulo apresentando os campos te?ricos em que a pesquisa
se fundamenta, os quais denominei de Campos Te?ricos de Investiga??o (CTI).
No cap?tulo 2 discorro sobre cada um dos Campos Te?ricos de Investiga??o,
introduzidos no final do primeiro cap?tulo. Nessa discuss?o procuro ligar os CTI
com a pesquisa. No cap?tulo 3 delimito e discuto as escolhas metodol?gicas com
base nos campos te?ricos em que a pesquisa se assenta. Ent?o, nos cap?tulos
4,5 e 6, apresento o corpus principal da pesquisa, ou seja, reconstruo a hist?ria do
c?lculo numa perspectiva de constru??o de modelos (quest?es respondidas) a
partir a dos problemas geradores (quest?es e aberto), analisando as contribui??es
dos gregos antigos ( cap?tulo 4), p?s-gregos, especialmente, a contribui??o dos
romanos, indus, ?rabes e as contribui??es na Idade M?dia (cap?tulo 5). Retomo o
renascimento europeu e as contribui??es dos fil?sofos/cientistas at? culminar com
o trabalho de Newton (cap?tulo 6). Finalmente, nas considera??es finais, relato
minhas impress?es sobre o desenvolvimento da pesquisa e de como asseguro
que a pergunta diretriz e os objetivos foram alcan?ados. Por ?ltimo, delineio uma proposta de curso de C?lculo Diferencial e Integral tendo como eixo os tr?s ?ltimos cap?tulos da tese
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