Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números

The present thesis is an analysis of Adrien-Marie Legendre s works on Number Theory, with a certain emphasis on his 1830 edition of Theory of Numbers. The role played by these works in their historical context and their influence on the development of Number Theory was investigated. A biographic study of Legendre (1752-1833) was undertaken, in which both his personal relations and his scientific productions were related to certain historical elements of the development of both his homeland, France, and the sciences in general, during the 18th and 19th centuries This study revealed notable characteristics of his personality, as well as his attitudes toward his mathematical contemporaries, especially with regard to his seemingly incessant quarrels with Gauss about the priority of various of their scientific discoveries. This is followed by a systematic study of Lagrange s work on Number Theory, including a comparative reading of certain topics, especially that of his renowned law of quadratic reciprocity, with texts of some of his contemporaries. In this way, the dynamics of the evolution of his thought in relation to his semantics, the organization of his demonstrations and his number theoretical discoveries was delimited. Finally, the impact of Legendre s work on Number Theory on the French mathematical community of the time was investigated. This investigation revealed that he not only made substantial contributions to this branch of Mathematics, but also inspired other mathematicians to advance this science even further. This indeed is a fitting legacy for his Theory of Numbers, the first modern text on Higher Arithmetic, on which he labored half his life, producing various editions. Nevertheless, Legendre also received many posthumous honors, including having his name perpetuated on the Trocadéro face of the Eiffel Tower, which contains a list of 72 eminent scientists, and having a street and an alley in Paris named after him

Natal, outra cidade : o papel da Intendência Municipal no desenvolvimento de uma nova ordem urbana(1904-1929)

The present work regards, as its subject, the management of the urban space. It aims to survey the role assumed by the Conselho de Intendência Municipal de Natal (Municipal Stewardship Council of Natal) in the formation of a new urban order between the years of 1904 and 1929. For a better comprehension of the object of research, the milestone of the time span analyzed in this work was receded to the year of 1890, specifically at the first chapter of this dissertation. In this chapter, we will turn our attention towards an analysis of the referred council, on the regulation of its operation, the relations of this institution with the state government and its mechanisms of action in the city, among other topics. In the next chapter, we will delve into an elite who administrated the city of Natal during the first republic, understanding that the analysis of the formation of a modern city project by the Municipal Stewardship undergoes the comprehension of those who leaded this institution. In the third chapter, we will examine the limits of the municipal management to put into practice its projects to the upraise of a new Natal, between the years of 1904 and 1921. The last chapter, on its turn, presents a new Stewardship, reformulated after a process of administrative streamlining, and a city that transforms itself, especially during the O Grady tenure by receiving major constructions, which alter its main features. We will regard, as the main resources of this study, articles from the daily newspapers A República (The Republic) and Diário de Natal (Daily Natal), dictums, announcements, laws, state decrees and the messages disclosed by the state government. To build a way of analysis, we make use of authors such as Anthony Giddens, Peter Burke and Laurent Vidal, among many others who discuss concepts related to the proposed theme