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

Entre veados, carneiros e formigas: conflito pela posse de terra na ribeira do Ceará-Mirim, e concepções de mentalidade possessória, 1725-1761

Shaping the Luso-Brazilian space in Portuguese America was through constant conflicts between different individuals and institutions. Regarding to land ownership, such conflicts were aggravated, depending on the individuals involved and their context. The captaincy of Rio Grande, there is conflict over land ownership Cidade dos Veados and Olho d' Água Azul and its stakeholders: priests of the Society of missionaries of the village Guajiru; indian mission Guajiru; and members of Carneiro da Cunha family. In 1725, the jesuit mission Guajiru requested a league of land at a place called Cidade dos Veados for the indians of his mission claiming that the land that the mission had was not sufficient for the subsistence of the same. In 1727, priest requested another league of land in place Olho d'Água Azul, stating that the mission had more than 192 couples. Both lands were properly required for the mission guajiru. however, in 1760, with the changes imposed by the indian directorate ombudsman responsible for investigating indigenous possessions realized that the indians did not occupy the two lands requested in the 1720s , due to the fact João Carneiro da Cunha has taken possession of the same. As a result, the impasse over land are ligth. This conflict over land ownership Cidade dos Veados and Olho d'Água Azul, we intend to highlight in particular the motivations and mindsets about possessory property of each party involved. We seek to understand the motivations of each group involved allowed the use of specific strategies and set out to try to take possession of the lands of the Cidade dos Veados e Olho d'Água Azul