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

Cuidado de si e hermenêutica do sujeito em Michael Foucault

The work, here present, has as its objective to present in a clear and distinct manner the object of study of Michel Foucault in his last years of teaching at the College de France, namely, the care of the self. We present the care of the self in its birth, in its origin, from the character Socrates and its development until the beginning of the Christian age. With a keen eye, we present Foucault with a work of return and rescue of the care of the self to the personal and academic discussions; we propose, from the self care, to the contemporary subject a problematization of their life so that from this questioning he creates for herself ways of life that are coherence, knowledge and care with which he has of must particular, his himself. Passing by the sources that served as the source of study for Foucault to sketch the birth of care of the self, we design the form with which Foucault has dealt with the documents that speak of the care of self. We present Socrates as one who by excellence ensures that the other will give birth to the forms of knowledge and care of the self or, in other words, we present the care of the self socratic-foucauldian as a constant worry of the other to pay attention to ways in which he conducts her life, it creates for themselves ways of being and, therefore, creates ethics of existence. We present, finally, the care of the self as the cause of continuous immanence of modes of subjectivation of the subject that configure themselves in a non-accepting a determined essence, but a continually updated form . The care of the self leads to a single relationship and educator of modes of subjectivation of the subject; he creates, on the dynamics of temporality, ethical ways of living, which are sustained by an internal coherence of the subject with herself; he admits no stationary nature in the training of the subject, always wants a more beautiful work of himself; he is not isolation, he needs and is made with the other. The care of the self is the principle and the telos of battles and conquests of the subject within his temporality and existence