 Let us also say for present purposes that a metrical geometry is one in which distance is a primitive concept, so line segments can be said to have the same length, congruent figures have corresponding sides equal in length, and geometrical transformations preserve lengths. We can also allow that similarities are allowed: these are transformations that produce scale copies of figures. (No theorem in Euclid’s Elements depends on the actual size of a figure: any theorem that applies to one figure applies to all its scale copies.)