SP Roseli Alves De Moura Um Estudo Sobre a Instituzioni Analitiche De

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SP Roseli Alves De Moura Um Estudo Sobre a Instituzioni Analitiche De Pontifícia Universidade Católica de São Paulo PUC - SP Roseli Alves de Moura Um estudo sobre a Instituzioni Analitiche de Maria Gaetana Agnesi: Álgebra e Análise na Itália setecentista Doutorado em Educação Matemática São Paulo 2017 Pontifícia Universidade Católica de São Paulo PUC - SP Roseli Alves de Moura Um estudo sobre a Instituzioni Analitiche de Maria Gaetana Agnesi: Álgebra e Análise na Itália setecentista Doutorado em Educação Matemática Tese apresentada à Banca Examinadora da Pontifícia Universidade Católica de São Paulo, como exigência parcial para obtenção do título de Doutor em Educação Matemática sob a orientação do Prof. Dr. Fumikazu Saito São Paulo 2017 Banca Examinadora ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ Dedico este trabalho ao meu pai e minha mãe! Nada a ser feito seria suficiente para demonstrar o quanto sou grata pela honra de ser filha deles! Autorizo exclusivamente para fins acadêmicos e científicos, a reprodução total ou parcial desta Tese por processos de fotocopiadoras ou eletrônicos. Assinatura:____________________________________Local e Data:__________ AGRADECIMENTOS Esta pesquisa não seria possível, sem o apoio institucional da Pontifícia Universidade Católica de São Paulo (PUC-SP) e da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), pela concessão da bolsa de estudos, sem a qual não poderia ter feito o curso de doutorado. Agradeço à todos os professores do Programa de Estudos de Pós-graduados em Educação Matemática da PUC-SP e, principalmente, ao professor Dr. Saddo, por seu apoio e estímulo, sempre. Ao meu orientador, professor Dr. Fumikazu Saito que, com incontestável competência e paixão pela pesquisa, soube orientar e conduzir este trabalho, além de estimular sempre à reflexões acerca da necessidade e, contribuição de pesquisas dessa natureza à Educação Matemática. Aos professores Arlete de Jesus Brito, Barbara Lutaif Bianchini e Nilson José Machado que, durante a qualificação, contribuíram com valiosas dicas e sugestões e, em especial, ao professor Gabriel Loureiro de Lima cuja revisão de alguns tópicos foi fundamental no sentido de auxiliar à abordagem epistemológica deste trabalho, considerada no século XVIII, mas com releitura no espaço e tempo do século XXI. Cabe também agradecer à Biblioteca Ambrosiana de Milão, na Itália, e seus bibliotecários, particularmente o Coordenador Dr. Nino Cellamaro que, não somente presencialmente, durante os meses de julho de 2013 e julho de 2015, mas ao longo de todo a pesquisa, auxiliou no levantamento e encaminhamento de materiais substanciais para o desenvolvimento deste trabalho. Palavras não seriam suficientes para agradecer o apoio de inúmeros amigos, mas notadamente Daniela Violato que, além de responsável pela revisão da tradução italiana necessária ao longo do pesquisa, esteve ao meu lado durante todo o percurso, sempre com uma palavra amiga... e a doce Camila Valala, pela força e estímulo, nesta fase final! Aos colegas do grupo de pesquisa Heema, pelas contribuições no meio do caminho e, principalmente à amiga Ana Rebeca Miranda Castillo, pelo esmero na revisão final, Regina Thaíse Ferreira Bento e Angela Maria dos Santos, companheiras de jornada, sempre ao lado, ora com entusiasmo, ora aconchego. A troca, a teia de emoções e sentimentos que se estabeleceu ao longo desse período, sem dúvidas, tem nos transformado.... graças a Deus! Agradeço a todos os amigos da Faculdade de Engenharia Industrial – FEI, em especial ao Prof. Aristóteles Antonio da Silva, eterno professor e colega de trabalho e ao Prof. Fábio Gerab, sempre com palavras de incentivo e lembrando que, na verdade, animus vincit omnia. Gratidão aos meus filhos, principalmente minha filha Mayra Moura, com a revisão da tradução inglesa, pais, irmãos e amigos! Perdão pela ausência; necessária... e acima agradeço à DEUS, que esteve ao meu lado por todo o tempo, e sempre há de estar! Vivo autem jam non ego; vivit vero in me Christus. (Gálatas, 2-20) Maria Gaetana Agnesi “Porque se chamavam homens Também se chamavam sonhos E sonhos não envelhecem Em meio a tantos gases lacrimogênios Ficam calmos, calmos Calmos, calmos, calmos... E lá se vai mais um dia...” Trecho da música “Clube da Esquina 2” Milton Nascimento - Lô Borges - Marcio Borges “Eu vejo um horizonte trêmulo Eu tenho os olhos úmidos Eu posso estar completamente enganado, posso estar correndo pro lado errado Mas a dúvida é o preço da pureza, e é inútil ter certeza...” Trecho da música “Infinita Highway” Humberto Gessinger RESUMO Neste trabalho apresentamos um estudo sobre a introdução da Álgebra e da Análise em Milão no século XVIII, tendo por foco a obra intitulada Instituzioni Analitiche ad uso della giuveniu Italiana, publicada por Maria Gaetana Agnesi (1718-1799) em 1748. Dividida em dois grandes volumes, a Instituzioni Analitiche abarca conhecimentos ligados à Álgebra e ao Cálculo, que começaram a ser disseminados naquela época. Esses novos campos de investigação matemática, entretanto, se desenvolveram e se disseminaram num cenário bastante complexo em que se entrelaçaram questões de ordem religiosa, política e econômica, e estavam estreitamente relacionadas ao conhecimento de uma nova ciência emergente. Assim, este trabalho tem como objetivos: contextualizar e identificar quais conhecimentos matemáticos foram mobilizados e abordados na obra de Agnesi. Além disso, buscamos entre outros pontos, apresentar alguns indícios que situam a Instituzioni Analitiche no processo que conduziu à especialização moderna. Para tanto, analisamos o primeiro volume de Instituzioni Analitiche, sobre a qual incidimos análises específicas. O estudo dessa obra, bem como a resolução de equação quadrática de Agnesi, revelou-nos o caráter multifacetado das matemáticas setecentistas, manifestado na predileção de Agnesi em publicar uma obra de matemática pura num contexto em que se destacavam estudos de matemáticas mistas. As questões de ordem epistemológica e matemática implicadas na obra de Agnesi apontam para o intrincado e complexo processo da construção do conhecimento matemático moderno propiciando uma visão mais contextualizada e atualizada de história que pode ser explorada por educadores matemáticos. Palavras-chave: História da Matemática. Educação Matemática. Matemáticas Mistas. Matemática Pura. Álgebra. Maria Gaetana Agnesi. ABSTRACT In this work we present a study on the introduction of the Algebra and Analysis in Milan in the eighteenth century, with the focus on the work entitled Instituzioni Analitiche ad uso della giuveniu Italiana, published by Maria Gaetana Agnesi (1718-1799) in 1748. Divided into two large volumes, the Instituzioni Analitiche includes knowledge related to Algebra and Calculus, which began to be disseminated at that time. These new fields of mathematical research, however, have developed and spread in a very complex scenario in which intertwined issues of religious, political and economic, and were closely related to the knowledge of a new emerging science. This work aims to: contextualize and identify which mathematical knowledge were mobilized and discussed the work of Agnesi. In addition, we seek among others, present some evidence to place the Instituzioni Analitiche in the process leading to modern expertise. Therefore, we analyzed the first volume of Instituzioni Analitiche on which we focus specific analyzes. The study of this work, as well as the quadratic equation solving Agnesi, showed us the multifaceted character of eighteenth-century mathematics, manifested in Agnesi predilection to publish a pure mathematical work in a context that stood out studies of mixed mathematics. The issues of epistemological and mathematics involved in the work of Agnesi point to the intricate and complex process of building the modern mathematical knowledge providing a more contextualized and updated view of history that can be exploited by mathematics educators. Keywords: Mathematic History. Mathematic Education. Mixed Mathematical. Pure Mathematical. Algebra. Maria Gaetana Agnesi. LISTA DE FIGURAS Figura 1 – Maria Gaetana Agnesi: Busto de Fraccaroli – Palazzo di Brera em Milão28 Figura 2 - Residência da Família Agnesi: Via Pantano, Milão ................................... 32 Figura 3 - Frontispício de Instituzioni Analitiche ........................................................ 52 Figura 4 - Recurso utilizado por Agnesi para definir problemas determinados com solução única ............................................................................................................ 99 Figura 5 - Recurso utilizado para definir problemas indeterminados: Ângulo inscrito na circunferência ..................................................................................................... 100 Figura 6 - Utilização da terceira e quarta proporcional ............................................ 104 Figura 7 - Cubo inscrito na esfera ........................................................................... 105 Figura 8 - Equação obtida por proporção entre segmentos .................................... 114 Figura 9 - Obtenção de lugar geométrico: Parábola ................................................ 115 Figura 10 - Representação geométrica equação de segundo grau: Casos I) e II) .. 131 Figura 11 - Representação geométrica equação de segundo grau: Casos III) e IV) ...............................................................................................................................
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