Sobre a obra Canon Doctrinae Triangulorum (1551) de Georg Joachim Rheticus e suas relações com o desenvolvimento da trigonometria

Abstract

The interest in the study of the work Canon Doctrinae Triangulorum (1551) arose from our readings, carried out in the Group of Studies and Research in History and Teaching of Mathematics (GEHEM), in the year 2020, when we initially comment on the work produced by the Austrian mathematician Georg Joachim Rheticus (1514 – 1574). When we started this research, we noticed few citations to the name of Rheticus, who was the only student of Copernicus and contributed to the publication of the work on heliocentrism, in the history of evolution on astronomy and trigonometry. Therefore, it allowed us to formulate hypotheses about the relationship between the Canon of Rheticus and the development of trigonometry, mainly in the 16th and 17th centuries. We decided to analyze the work registered as Canon Doctrinae Triangulorum (1551) by the mathematician Rheticus, with a view to establishing the relationships between the studied work and the development of trigonometry in the 16th and 17th centuries. For this, we carried out a specialized bibliographical research, which we organized according to the methodological diagram suggested by Chaquiam (2022), as a guide for the historical development of the research, as we consider it important to highlight the information suggested by Brandemberg (2021) and Chaquiam (2022); and documentary research, from primary and secondary sources, seeking to collect qualitative data regarding the analysis of the Canon in order to establish relationships between the work and the development of trigonometry. As a result, we emphasize that the work contributed to the advancement of studies of trigonometric ratios, as Rheticus was the first to present the six trigonometric ratios through the sides of right triangles. The relations that we highlight, with the development of trigonometry, are those of influences with the works developed by Valentin Otto (1550 – 1603), Bartholomaeus Pitiscus (1561 – 1613), Francesco Maurolico (1494 - 1575) and Françóis Viète (1540 - 1603), who expanded studies on trigonometric tables until the development of logarithm tables in the 17th century. A possible future development of this research would be to verify how Rheticus ended up in textbooks.