 Euclid’s treatment of geometry has, through the ages, been celebrated as a perfect deductive presentation of a science, and certainly Euclid made great efforts to obtain a most careful logical chain of truths. Book I in particular is impressive (see Lambert 1786, Mueller 1981). Yet his proof-method gives a central role to diagrams, for which reason Euclid’s work came under severe criticism in the late nineteenth century. This is because, from the early eighteenth century, there was a gradual dominance of algebraic methods and a process of de-geometrization of mathematics, which evolved into the so-called “arithmetization” of mathematics. Diagrams were demoted to the role of mere auxiliaries in mathematical reasoning, and a careful logical presentation of axioms and proofs was implemented. One result of this movement would be Hilbert’s work, examined below.