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

Deus, mente e mundo: sobre os conceitos de complicatio, imago e explicatio a partir do diálogo de mente de nicolau de cusa

This work deals with the way how the three themes of traditional metaphysics, namely, God, man, and the world, are rethought through the philosophical speculation of German cardinal Nicholas of Cusa (1401-1464). Due to the comprehensiveness of this subject, our dissertation had as a starting point and constant reference the book that the philosopher wrote in 1450, Idiota. De mente, the second written work that makes up the series of the Idiota (Idiotae libri), whose discussion is developed around the theme of the human mind. From the dialogue of the mind we have built our reflection on some issues and theoretical foundations presented in Idiota. De sapientia and De docta ignorantia, extending it to little more than that. According to Nicholas of Cusa, the human mind, in its creative character in the image of the divine mind, transcends the purely functional considerations commonly assigned to it, that is, those that regard its cognitive nature and epistemological role. In addition to these aspects, Cusanus understands the humana mens as a point of articulation of two other main themes of his metaphysics: God and the world. In this context, through the concepts of complicatioexplicatio and imago, as well as with the intercession between the themes of man as imago Dei and the reason of the microcosm, we present here an introduction to Cusan metaphysics