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

Corpo e fronteira: o diário de Samuel Fritz e a conquista do espaço amazônico

Considering that the Jesuitical tradition which Father Samuel Fritz belonged, has a clear political and institutional dimension that reveals itself in the missionary initiative placed since the Trento Council, his journal is a experience story as missionary at Maynás region during the period from 1686 until 1725. In his narrative, a series of data related to the conquer of Amazonia, conflicts among the Iberic Kingdoms and french, dutches and british, transformation of culture and space close the period of the Madrid Deal. I´ll explore the men and space relationship, in this case, the missionary in his special practice, therefore an effective and geometrical politic for border control was only applied at 1750 with reformist governments and that Amazônia was, until now, an object of autonomous initiatives, not being until now a priority focused state politics action like the ones in the central regions (silver mines) and that the missionary action of Samuel Fritz represented ant that moment represented the most important border advance to the Spanish Kingdom, coinciding with the end of the borders previously set in Madrid and Santo Idelfonso, I´ll put the question of how and with which politics the experience of Fritz in Maynás could represent an advance about Amazônia space. Then I´ll approach the problem about three aspects that are chapters: The first one was focused to the Iberic Kingdoms atlantic politics and the internal geopolitical relationships they created as the centre and the border emerging a new order; in the second chapter I studied the special transformation cause by the encounter and conflicts between the Indian and European order generating a new organization; in the third chapter I´ll examined the political border of the state and the emergency of the missionary body as an institution, with the tradition and missionary action as support, or not, to the exploration of the east border of Spanish America influencing the delimitation process of the border between Portugal and Spain