From Practical to Pure Geometry and Back

The purpose of this work is to address the relation existing between ancient Greek (planar) practical geometry and ancient Greek (planar) pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which are basically explicit in definitions, like that of segments (straight lines) in Euclid‘s Elements. Then, we will address how in pure geometry we, so tospeak, ―refer back‖ to practical geometry. This occurs in two ways. One, in the propositions of pure geometry (due to the accompanying figures). The other, when applying pure geometry. In this case, geometrical objects can represent practical figures like, e.g., a practical segment.