Knowledge of a mathematical nature mobilized by the use of John Hadley's (1682-1744) Reflective Octant

Abstract

Since ancient times, mathematics has played a crucial role in the development of society. Studies on the History of Mathematics indicate that Mathematics itself was not an institutionalized area until the 19th century, and, before that, it was used in areas that we identify as navigation, astronomy, engineering, among others. During the 17th and 18th centuries it was no different, mathematics, for example, appears associated with the construction and use of instruments used to meet social needs, as in the case of the development of navigation. From this perspective, the present work aims to highlight some of the knowledge, with an approach of a mathematical nature, but also others such as physical and geographic, which are mobilized during the use of John Hadley's Reflective Octant (1682-1744). To this end, qualitative research was carried out using bibliographic and documentary procedures, to search and survey sources that provided data on the context of navigation between the 17th and 18th centuries and to evaluate documents, written by the Hadley brothers, on the manipulation of Octante in navigation. As a result, I presented a story about the Hadley brothers making the connection with the development of the Reflective Octant, as well as some knowledge that comes from its use, such as: the use of geometric concepts, such as supplementary and complementary angles and internal and external angles. a triangle, as well as the properties of mirror reflections and location of navigation on the high seas.