 Theorem I.4 is interesting in another way. Theorem I.2 carries a scrupulous, and by no means obvious, proof that a given line segment in a plane may be copied exactly with one of its end points at any prescribed point in the plane. Theorem I.4 properly requires a proof that an angle may likewise be copied exactly at an arbitrary point, but this Euclid cannot provide at this stage (one is given in I.23, which, however, builds on these earlier results). He therefore gave a bald claim that one triangle may be copied exactly in an arbitrary position, which makes one wonder why such care was expended on I.2. In fact, the whole concept of motion of figures was to become a prolonged topic of discussion in Arabic/Islamic times. (On deduction in Euclid, see Mueller 1981.)