This dissertation traces the reception of Greek mathematics by practicing mathematicians in England and France, ca. 1580-1680. The period begins with the newly widespread availability of works by Pappus, Apollonius, and Diophantus; it concludes with the invention of calculus by Isaac Newton and Gottfried Leibniz. The dissertation focuses on a philological imaginary created by François Viète (fl. 1580-1600) that I call “the myth of Greek algebra”: the belief that the ancient Greek geometers concealed their heuristic method and only presented their results. This belief helped mathematicians accommodate ancient Greek works to their own mathematical ends; it helped mathematicians sustain the relevance of Greek texts for their own inventions. My study focuses on Viète, Rene Descartes, John Wallis, Isaac Newton, and Gottfried Leibniz: I show how these mathematicians continually renovated the relationship between ancient and modern mathematics in order to maintain continuity between their discoveries and the past. In order to do so, I argue, they became increasingly conscious of their professional identity as mathematicians, and they asserted their unique right—over philologists and philosophers—to interpret ancient mathematical texts. Mathematical community with the ancients was purchased at the cost of community with one’s non-mathematical contemporaries.

Orientador: Antonio Vicente Marafioti Garnica / Coorientador: Antonio Vicente Marafiotti Garnica / Banca: Heloisa da Silva / Banca: Luzia Aparecida de Souza / Resumo: Este trabalho apresenta a tradução integral dos Manuscritos da Aritmética Elementar de Charles Sanders Peirce e algumas notas de pesquisa criadas com a intenção de subsidiar uma Hermenêutica dos Manuscritos traduzidos. Estes Manuscritos foram produzidos no século XIX e não foram publicados e nem mesmo concluídos pelo autor, só chegando até nós devido ao trabalho de Carolyn Eisele, pesquisadora quem os editou e publicou no ano de 1976. A elaboração das notas foi inspirada no referencial metodológico da Hermenêutica de Profundidade de John B. Thompson. Nestas notas de pesquisa tematizamos a metodologia de pesquisa qualitativa, da historiografia e do campo de pesquisa da História da Educação Matemática; a Hermenêutica de Profundidade; os Paratextos Editoriais de Gérard Genette; trabalhos anteriores ao nosso que se inspiraram nos referenciais teórico-metodológicos da Hermenêutica de Profundidade e/ou dos Paratextos Editoriais para criação de suas metodologias de pesquisa; o processo de tradução dos Manuscritos; a biografia de Charles Sanders Peirce; a biografia da pesquisadora Carolyn Eisele; acontecimentos da História dos Estados Unidos e da Educação Estadunidense no período em que Peirce viveu; acontecimentos que envolveram a produção, arquivo e divulgação dos Manuscritos de Peirce; e sobre nossa experiência com a pesquisa. / Abstract: In this work we present the complete translation of the Primary Arithmetic's Manuscripts of Charles Sanders Peirce and some research notes created with the intention of subsidizing a Hermeneutics of the translated Manuscripts. These Manuscripts were produced in the nineteenth century and were neither published nor concluded by the author, coming to us only due to the work of Carolyn Eisele, a researcher whom organized and published them in the year of 1976. The preparation of the notes was inspired by the methodological referential of the Hermeneutics of Depth of John B. Thompson. In these research notes we discuss the qualitative research methodology, the historiography and the History of Mathematics Education research field; the Hermeneutics of Depth; the Paratexts by Gérard Genette; previous works that were inspired by the theoretical-methodological references of Hermeneutics of Depth and/or of Paratexts to create their research methodologies; the Manuscripts translation process; the Charles Sanders Peirce's biography; the Carolyn Eisele's biography; events of the United States History and of the United States Education in the period when Peirce lived; events that involved the production, archiving and dissemination of the Peirce's Manuscripts; and our experience with the research. / Mestre

Orientador: Marisa da Silva Dias / Banca: Fumikazu Saito / Banca: Nelson Antonio Pirola / Resumo: Esta dissertação foi desenvolvida a partir do estudo de um tratado intitulado The Trigonall Sector. A obra foi publicada por John Chatfeilde, em 1650, e mostra a descrição e o uso de um instrumento matemático chamado setor trigonal. O documento apresenta relações geométricas e trigonométricas verificadas nas propriedades dos triângulos, incluindo senos, tangentes, secantes, como também cordas e relações de proporção. O objetivo geral foi investigar o movimento do pensamento de estudantes do ensino médio na formação dos conceitos inerentes ao uso do instrumento setor trigonal e seu respectivo tratado em uma atividade didática. A pesquisa é exploratória, orientada por uma interface entre história e ensino de matemática fundamentada na relação entre o movimento do pensamento na formação de conceito e o contexto no qual os conceitos foram desenvolvidos. Realizou-se estudo sobre a história de instrumentos matemáticos, o tratado e o próprio instrumento, a partir dos quais inferem-se potencialidades didáticas que desencadearam a realização de uma atividade orientadora de ensino com estudantes do ensino médio de uma escola pública. A análise das ações dos estudantes pautou-se na perspectiva lógico-histórica e dos pensamentos empírico e teórico. Verificou-se que a atividade orientadora de ensino proporcionou um diálogo entre os conhecimentos matemáticos de uma época com os atuais, o que permitiu aos participantes mobilizar conceitos matemáticos durante a atividade e auxiliá-los na com... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This dissertation was developed from a study of a treatise, titled The Trigonall Sector. This work was published by John Chatfeilde, in 1650, and shows the description and use of a mathematical instrument called trigonal sector. The document presents geometric and trigonometric relations verified in the properties of triangles, including sines, tangents, secants, as well as strings and proportion ratios. The general objective was to investigate the thinking process of students from high school when formulating inherent concepts to the use of the trigonal sector instrument and its respective treatise in a didactic activity. The research is exploratory, oriented by an interface between history and the teaching of Mathematics, based in a relation between the thinking process in forming concepts and the context in which the concepts were developed. It was conducted a study on the history of mathematical instruments, the treatise and the instruments themself, from where it is inferred didactic potentialities which resulted in the performance of an oriented teaching activity with high school students from a public school. The analyses of students' actions were guided by a logic-historical perspective and by empirical and theoretical thinking. It was verified that this activity provided a dialogue between mathematical knowledge from a time with the present day, which allowed to the participants to mobilize mathematical concepts during the activity and assist them in the comprehensio... (Complete abstract click electronic access below) / Mestre

Mathematics of the Islamic medieval world is still not sufficiently studied. As a result, a goldmine of Islamic medieval books and materials lie unexplored. One manuscript that certainly deserves attention is al-Bāhir fi’l-Jabr (The Shining Treatise on Algebra) of al-Samaw’al ibn Yahya al-Maghribi, a twelfth century mathematician. Al-Bāhir fi’l-Jabr is a manuscript written in Arabic and has never been translated except for a few excerpts in French. The purpose of this study was to explore the mathematical and pedagogical contribution of al-Samaw’al through an analysis of al-Samaw’al’s mathematical techniques and methods in al-Bāhir fi’l-Jabr. Moreover, the treatise provides a precise description of the “arithmetization of algebra”, and gives an accounting of the original ideas of another mathematician, al-Karaji, whose original documents have been lost. To develop a comprehensive picture of al-Samaw’al’s mathematical techniques and methods in al-Bāhir fi’l-Jabr (and his contribution to algebra in particular) this research has been based mainly on a careful analysis of al-Samaw’al’s manuscript in MSS Aya Sofia numbered 2718 (116ff), stored in the Suleymaniye library (Istanbul, Turkey). This study of al-Bāhir fi’l-Jabr focuses on an overview of how al-Samaw’al dealt with signed numbers, exponents and polynomial operations. Furthermore, this study describes the al-Samaw’al’s “method of the tables,” certain algorithms he employed, as well as his work on the binomial theorem, binomial coefficients, and the tabular arrangement known today as Pascal’s triangle. Most importantly, the study attempts to show the pedagogical approaches of al-Samaw’al.

Submitted by Marlene Aparecida de Souza Cardozo (mcardozo@pucsp.br) on 2017-01-10T10:40:51Z No. of bitstreams: 1 Arnaldo Aragão Santos.pdf: 2425915 bytes, checksum: dd9b7096a2a82c79df00dbc38463f185 (MD5) / Made available in DSpace on 2017-01-10T10:40:51Z (GMT). No. of bitstreams: 1 Arnaldo Aragão Santos.pdf: 2425915 bytes, checksum: dd9b7096a2a82c79df00dbc38463f185 (MD5) Previous issue date: 2016-11-01 / Secretaria de Educação do Estado de São Paulo - SEE / The study undertaken consists of a proposal for reflection on the Jean Etienne Montucla’s work, History of Mathematics, written in the mid-eighteenth century. In this sense, based on analysis of documents, approaches have been developed within the spheres of analysis in the history of science. Although intriguing, the particularities of the writing in History of Mathematics have not been treated enough by their historians who, by the way, barely discuss about their approaches and intentions before the twentieth century. To contextualize the work of Montucla, permeated by the French editorial development, specially the contemporary encyclopaedic genre and secularization of intellectual activities of his time, we seek to contribute to the research on the History of Mathematics and its historiography to seek connections that can be established between the historical development of mathematical knowledge and his writing. In this order, in an attempt to revisit the work of Montucla, we gather efforts to locate her before their relations and intellectual motivations of the mid-eighteenth century. / O estudo empreendido consiste em uma proposta de reflexão sobre a obra História das Matemáticas, de Jean Etienne Montucla, escrita em meados do século XVIII. Nesse sentido, com base na análise dos documentos, foram desenvolvidas abordagens dentro das esferas de análise em história da ciência. Apesar de intrigante, as particularidades da escrita da história da matemática não têm sido muito tratadas pelos historiadores que, por sinal, pouco discutem sobre suas abordagens e intencionalidades anteriores ao século XX. Ao contextualizar a obra de Montucla, permeada pelo desenvolvimento editorial francês, com destaque para o gênero enciclopédico contemporâneo e a secularização das atividades intelectuais de seu período, procuramos contribuir com as investigações sobre a História da Matemática e sua historiografia ao buscar conexões que podem ser estabelecidas entre o desenvolvimento histórico do conhecimento matemático e sua escrita. Nesse intuito, na tentativa de revisitar a obra de Montucla, reunimos esforços para localizá-la diante de suas relações e motivações intelectuais de meados do século XVIII.