Euclid’s in Practice: A treatise on Foundation and construction of Pantometers in 17th century Spain

Abstract

At the beginning of the seventeenth century, the Jesuit Christoph Clavius (1537-1612) -a competent and well-known mathematician- began his Practical Geometry (Mainz, 1606) with two chapters devoted to the construction and use of two mathematical instruments. Thus, in addition to the common quadrant, an instrument for easily dividing any line into any number of equal or proportional parts, that he called Instrumentum Partium -later pantometer- became part of the academic mathematics teaching. This paper looks at a 17th-century Spanish unpublished anonymous manuscript -probably a course- on the construction and use of sectors from the viewpoint of its contribution to the development of the arithmetization of geometry by means of the numerical consideration of continuous magnitudes as quantities. The author bases the instrumental operability of sectors -that surpassed geometric methods or arithmetic calculations in terms of time and errors savings- on Euclid’s Elements, especially Book VI. As for incommensurability, the reduction of incommensurable quantities to the nearest commensurable quantities is accepted, for it is possible without noticeably error by the senses and irrelevant in practice.