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

A Produção do Flagelo : a re-produção do espaço social da seca na cidade de Mossoró (1877-1903-1915)

The great droughts re- produced spaces in the city of Mossoró / RN in the end of the nineteenth century to the beginning of the twentieth century. Its dimension exceeds the climatic effects becoming social locus when advances over the political and economic sectors, social and cultural of the North / Northeast Brazilian societies during that period. This way, analyzing the re-production of social space in episodes of Mossoró‟s droughts is our toil. So try to reveal each segment, route and aspect of production of space in its size and interface between the perceived, conceived and lived, and subjects related to it - refugees, population and authorities - during the droughts of 1877, 1903 and 1915 within Mossoró city. Therefore, issues such as the constitution and representation of the city and social space in the terrifying experience of the drought of 1877, the production of fixed objects and flows of the urban web through of migrant labor, attempts to control, discipline and spatial planning and ways to resistance to these charges in daily sphere are key issues addressed in this work. For this we use diverse sources as minutes of the city council, reports from provincial presidents, media, memory books and others that sustain us in building our narrative and problematic. This way, the spatial production of Mossoró‟s droughts reveals itself in the field of relations and political-economic transformations and sociocultural, inextricably, that shapes and mobilizes your own social space