At base, Euclidean space has little concern with coordinates and numbers but much concern with figures and containers. In Euclid's Elements, the primary geometry textbook for engineering sciences, the definition of a figure makes no mention of dimensions or the coordinates that Descartes instrumented as Euclidean space. Euclid defines a figure as ‘that which is contained by any boundary or boundaries’ (Euclid 2012, 1). A figure could be a circle, a square, a triangle, and so on, but not a line or a surface extended indefinitely, since those have no endpoints or extremities. This definition relies on preceding ones, many of which rely on even more elementary propositions and line-drawing; for example, ‘Definition 2: A surface is that which has length and breadth only’ (Euclid 2012, 1).

Figures in Euclid's Elements are, broadly speaking, containers to be mixed together to construct new containers. The propositions of the Elements are, in practice, instructions on how to use the definitions, postulates and previous propositions in combination to make figures (such as Figure III.1): ‘Proposition 1: On a given finite straight line to construct an equilateral triangle’ (Euclid 2012, 3). The propositions are figurative in Euclid's sense of the figure in that they are constructed using a compass and ruler to draw figures. The propositions, even those concerning number rather than geometry, are figured out using lines as boundaries. For Euclid, figures contain other figures or containers.