Practical Mathematics

Abstract

The chapter shows that the characteristic pattern of interrelations between learned and practical knowledge in the field of practical mathematics can be summarized by the following features: (1) All of the various domains of practical mathematics – surveying as well as higher geodesy, practical astronomy, and mathematical geography – were related to one or several mathematical theories. (2) Practical surveying in the realm of civil or military engineering as well as of mining explicitly or (more usually) implicitly used suitable results of learned mathematics, regardless of their justification or function in Euclid’s theory building. This pragmatic and eclectic use of learned mathematics was characteristic of all fields of practical geometry. (3) The standard tasks of early modern practical astronomy as well as mathematical geography were intelligible and solvable only in the inherited framework and coordinate system of a mathematical model of heavens and the Earth. (4) Learned mathematics remained largely untouched by developments in practical surveying or other domains of practical geometry. In contrast, developments in practical astronomy and geography led to fundamental revisions of the underlying mathematical model of celestial movements and thereby eventually to the destruction of the classic cosmology inherited from Greek Antiquity.KeywordsComputing booksMathematical instrumentsSurveyingAngular measurementAstronomyGeographyCartographyGeodesy