A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

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