A obra de triangulis omnimodis libri quinque de Johann Müller Regiomontanus (1436 1476): uma contribuição para o desenvolvimento da trigonometria

Trigonometry, branch of mathematics related to the study of triangles, developed from practical needs, especially relating to astronomy, Surveying and Navigation. Johann Müller, the Regiomontanus (1436-1476) mathematician and astronomer of the fifteenth century played an important role in the development of this science. His work titled De Triangulis Omnimodis Libri Quinque written around 1464, and published posthumously in 1533, presents the first systematic exposure of European plane and spherical trigonometry, a treatment independent of astronomy. In this study we present a description, translation and analysis of some aspects of this important work in the history of trigonometry. Therefore, the translation was performed using a version of the book Regiomontanus on Triangles of Barnabas Hughes, 1967. In it you will find the original work in Latin and an English translation. For this study, we use for most of our translation in Portuguese, the English version, but some doubt utterance, statement and figures were made by the original Latin. In this work, we can see that trigonometry is considered as a branch of mathematics which is subordinated to geometry, that is, toward the study of triangles. Regiomontanus provides a large number of theorems as the original trigonometric formula for the area of a triangle. Use algebra to solve geometric problems and mainly shows the first practical theorem for the law of cosines in spherical trigonometry. Thus, this study shows some of the development of the trigonometry in the fifteenth century, especially with regard to concepts such as sine and cosine (sine reverse), the work discussed above, is of paramount importance for the research in the history of mathematics more specifically in the area of historical analysis and critique of literary sources or studying the work of a particular mathematician

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