ABSTRACT
In Part I the subject matter of the Elements has been shown to consist of figures which are the most general type of ‘bounded thing’. Specific figures then provided instances of the essentially indeterminate relationship discovered between limited plane surfaces and their boundaries by the Definitions of Book I. This subject matter is expressed in propositions which take the form of both ‘constructions’ and ‘demonstrations’. By contrast the subject matter of Descartes' Géométrie was seen to be a certain kind of line or curve (so-called ‘geometric’ curves as distinguished from ‘mechanical’ ones) expressed in propositions which are principally constructions, while in Hilbert's Grundlagen der Geometrie the subject matter is the logical relationships between axioms and theorems as expressed in propositions which are principally demonstrations.
