O quinto postulado de Euclides. História e desdobramentos nos fundamentos da matemática

• Ano de defesa: 2015
• Autor(a) principal: Pinto, Clarissa Rosa
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Roraima; Brasil; PRPPG - Pró-reitoria de Pesquisa e Pós-Graduação; PROFMAT - Programa de Mestrado Nacional Profissional em Matemática; UFRR
• Palavras-chave em Português: Problema das paralelas; Os elementos de Euclides; O quinto postulado; Método axiomático; Axiomatic Method; Problem of parallels; The Elements of Euclid; The Fifth Postulate; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.ufrr.br:8080/jspui/handle/prefix/730

In this dissertation, we present the results of a bibliographic research about the so-called Problem of Parallels. Euclid’s fifth postulate, since its appearance in his monumental opus The Elements, raised suspicions and controversies and led to numerous researches that spread abroad since its publication until the nineteenth century, when appear the non-Euclidean Geometries and it was perfectly clarified the problem’s essence. This story, emotional and highly illustrative of the nature of the axiomatic method, had important consequences in Mathematical Foundations, especially, consolidating the principles of the Formalist School as paradigms of the construction of Mathematics.