Petrus Ramus’ baculum and its use for depth measurement

Abstract

The history of mathematics offers several didactic resources and strategies for mathematics teaching, contributing to the construction of mathematical knowledge. Among these available resources, the mathematical instruments contained in old treaties are stand out those situated in the 16th and 17th centuries. The Via Regia ad Geometriam, is one of those texts, which it was published in Latin in 1569, by the French Petrus Ramus, translated into English and published by William Bedwell, in 1636. This document, which deals with the “art of measuring well”, brings an instrument used by surveyors of the time, called baculum. The description of the manufacture and different situations of use of baculum, for measuring distances (lengths) and heights, it is presented in chapter nine of the treatise. In this sense, this article aims to present mathematical knowledge based on a situation proposed by Petrus Ramus, for the use of his baculum, related to depth measurement. Thus, a qualitative documentary methodology was used, based on translation, comprehension (historical and mathematical) and discussion of the excerpt, which guided the search for didactic potentialities of using the baculum for this situation. During the study, it was noticed that, for this specific situation, the author names the depth as reverse height (Eversa altitudo), in another words, he considers it to be a height below the ground, focused on measuring wells, deep holes and rivers. With regard to the mathematical concepts arising from the application of this situation, it is clear that perpendicularity, parallelism, properties of the right triangle, similarity of triangles, among others, are used in the handling of the baculum and that both can be directed to the development of some skills of the Base National Common Curriculum (BNCC) in Elementary Education. However, it is considered that, after a real measurement of a depth, using the instrument, other concepts can be perceived and added to the didactic potentialities, aiming, thus, to establish an articulation between history and the teaching of mathematics.